Question 1

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​
P = 3,000, r = 5, t = 3, m = 4
​

Accepted Answer

The formula for the periodic payment R is:R = P * (r/m) / (1 - (1 + r/m)^(-mt))Plugging in the given values, we get:R = 3000 * (0.05/4) / (1 - (1 + 0.05/4)^(-4*3))= 3000 * 0.0125 / (1 - (1.0125)^(-12))= 3000 * 0.0125 / (1 - 0.7490)= 3000 * 0.0125 / 0.2510= 3000 * 0.05 / 1= $150Therefore, the periodic payment required to amortize the loan is $150.

Question 2

A sum of $110,000 is to be repaid over a 9-year period through equal installments made at the end of each year. If an interest rate of 11%/year is charged on the unpaid balance and interest calculations are made at the end of each year, determine the size of each installment so that the loan (principal plus interest charges) is amortized at the end of 9 years. Round your answer to the nearest cent. ​

Accepted Answer

The answer of A sum of $110,000 is to be...

Question 3

Determine whether the statement is true or false; explain why.
​
The present value of an annuity can be found by multiplying the future value by compound interest multiplier -  .

Accepted Answer

The answer of Determine whether the statement is true or...

Question 4

From age 30 to age 40, Jessica deposited $100 at the end of each month into a tax-free retirement account. She made no withdrawals or further contributions until age 65. Alex made deposits of $350 into his tax-free retirement account from age 40 to age 65. If both accounts earned interest at the rate of 5%/year compounded monthly, who ends up with a bigger nest egg upon reaching the age of 65, Jessica or Alex?

Accepted Answer

The answer of From age 30 to age 40, Jessica...

Question 5

Luis has $150,000 in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to roll over his assets to a new account. Luis also plans to put $1,000/quarter into the new account until his retirement 19 yr from now. If the account earns interest at the rate of 6%/year compounded quarterly, how much will Luis have in his account at the time of his retirement? Please round the answer to the nearest cent.
(Hint: Use the compound interest formula and the annuity formula.)
$__________

Accepted Answer

The answer of Luis has $150,000 in his retirement account...

Question 6

Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​
S = 280,000, r = 11, t = 26, m = 13
​

Accepted Answer

The periodic payment R can be calculated using the future value of an annuity formula: $ R = \frac{S \cdot \frac{r/m}{(1 + r/m)^{mt} - 1}}{(1 + r/m)^{mt} - 1} $. Plugging in the values S = 280,000, r = 0.11, t = 26, m = 13, the calculation gives R approximately equal to $145.77.

Question 7

Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​
S = 20,000, r = 4, t = 7, m = 4
​

Accepted Answer

The formula for periodic payments is:

R = (S*i)/(1-(1+i)^(-n))

where i = r/100m is the interest rate per period and n = mt is the total number of periods.

Plugging in the values given, we get:

i = 0.04/4 = 0.01 (interest rate per period)
n = 4*7 = 28 (total number of periods)
S = 20000 (target sum)

R = (20000*0.01)/(1-(1+0.01)^(-28))
R = $622.49

Therefore, the best choice is B.

Question 8

Suppose payments were made at the end of each quarter into an ordinary annuity earning interest at the rate of 12%/year compounded quarterly. If the future value of the annuity after 3 years is $40,000, what was the size of each payment? Round your answer to the nearest cent. ​

Accepted Answer

The future value of an ordinary annuity is given by the formula:FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)where:P is the payment amountr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:FV = $40,000r = 12% = 0.12n = 4 (since interest is compounded quarterly)t = 3Substituting these values into the formula, we get:$40,000 = P * ((1 + 0.12/4)^(4*3) - 1) / (0.12/4)Solving for P, we get:P = $2,818.48Therefore, the size of each payment was $2,818.48.

Question 9

A state lottery commission pays the winner of the "Million Dollar" lottery 10 installments of $100,000/year. The commission makes the first payment of $100,000 immediately and the other  payments at the end of each of the next 9 yr. Determine how much money the commission should have in the bank initially to guarantee the payments, assuming that the balance on deposit with the bank earns interest at the rate of 15%/year compounded yearly. Please round the answer to the nearest cent.
(Hint: Find the present value of an annuity.)
$__________

Accepted Answer

The answer of A state lottery commission pays the winner...

Question 10

Karen has been depositing $150 at the end of each month in a tax-free retirement account since she was 20. Matt, who is the same age as Karen, started depositing $200 at the end of each month in a tax-free retirement account when he was 25. Assuming that both accounts have been and will be earning interest at the rate of 6%/year compounded monthly, who will end up with the larger retirement account at the age of 65, Karen or Matt?

Accepted Answer

The answer of Karen has been depositing $150 at the...

Question 11

Find the present value of the ordinary annuity. Please round the answer to the nearest cent.
$2,000 per semiannual period for 8 yr at 12%/year, compounded semi-annually
P = $__________

Accepted Answer

The answer of Find the present value of the ordinary...

Question 12

Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​
S = 110,000, r = 4.5, t = 22, m = 4
​

Accepted Answer

The answer of Find the periodic payment R required to...

Question 13

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​
P = 23,000, r = 3, t = 12, m = 3
​

Accepted Answer

The formula for the periodic payment R is given by:  $$ R = \frac{P \cdot \frac{r/m}{1 - (1 + r/m)^{-mt}}}{1 - (1 + r/m)^{-mt}} $$  Substituting the given values:  $$ P = 23000, \ r = 0.03, \ t = 12, \ m = 3 $$  $$ R = \frac{23000 \cdot \frac{0.03/3}{1 - (1 + 0.03/3)^{-36}}}{1 - (1 + 0.03/3)^{-36}} $$  Calculating this gives R approximately equal to $763.93.

Question 14

Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 10%/year compounded monthly. If the future value of the annuity after 10 years is $70,000, what was the size of each payment? Round your answer to the nearest cent. ​

Accepted Answer

Using the formula for future value of an ordinary annuity:

FV = R(((1 + r/n)^(nt) - 1)/(r/n))

where FV is the future value of the annuity, R is the size of each payment, r is the annual interest rate (10%), n is the number of compounding periods per year (12), and t is the number of years (10).

Plugging in the values, we get:

$70,000 = R(((1 + 0.1/12)^(12*10) - 1)/(0.1/12))

Solving for R, we get:

R = $341.72

Therefore, the best choice is B.

Question 15

Pierce Publishing sells encyclopedias under two payment plans: cash or installment. Under the installment plan, the customer pays $21/month over 3 yr with interest charged on the balance at a rate of 15%/year compounded monthly. Find the cash price for a set of encyclopedias if it is equivalent to the price paid by a customer using the installment plan. Please round the answer to the nearest cent.
$ __________

Accepted Answer

The answer of Pierce Publishing sells encyclopedias under two payment...

Question 16

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​
P = 80,000, r = 9, t = 12, m = 2
​

Accepted Answer

We can use the formula for periodic payment R:

R = P((r/m)(1+(r/m))^mt)/(((1+(r/m))^mt)-1)

Plugging in the given values:

R = 80000((0.09/2)(1+(0.09/2))^(2*12))/(1+(1+(0.09/2))^(2*12)-1)

R = 5518.96 (rounded to the nearest cent)

Therefore, the best choice is C.

Question 17

Find the amount (future value) of the ordinary annuity. Please round the answer to the nearest cent.
$200/month for  yr at 7%/year, compounded monthly
S = $ __________

Accepted Answer

The answer of Find the amount (future value) of the...

Question 18

Lauren plans to deposit $8,000 into a bank account at the beginning of next month and $200/month into the same account at the end of that month and at the end of each subsequent month for the next 3 yr. If her bank pays interest at the rate of 7%/year compounded monthly, how much will Lauren have in her account at the end of the 3 yr? (Assume she makes no withdrawals during the 3-yr period.) Please round the answer to the nearest cent.
$__________

Accepted Answer

The answer of Lauren plans to deposit $8,000 into a...

Question 19

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​
P = 60,000, r = 10.5, t = 29, m = 10
​

Accepted Answer

We can use the formula:
R = P * (r/m) * (1 + r/m)^(mt) / [(1 + r/m)^(mt) - 1]

Plugging in the values, we get:
R = 60000 * (10.5/100/10) * (1 + 10.5/100/10)^(10*29) / [(1 + 10.5/100/10)^(10*29) - 1]
R = $662.01

Therefore, the closest option is C, with R = $662.01.

Question 20

Suppose payments will be made for  years at the end of each semiannual period into an ordinary annuity earning interest at the rate of 8.5%/year compounded semiannually. If the present value of the annuity is $40,000, what should be the size of each payment? Round your answer to the nearest cent. ​

Accepted Answer

The answer of Suppose payments will be made for ...

Quiz 5: Mathematics of Finance

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. P = 3,000, r = 5, t = 3, m = 4

Determine whether the statement is true or false; explain why. The present value of an annuity can be found by multiplying the future value by compound interest multiplier - .

Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. S = 280,000, r = 11, t = 26, m = 13

Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. S = 20,000, r = 4, t = 7, m = 4

Suppose payments were made at the end of each quarter into an ordinary annuity earning interest at the rate of 12%/year compounded quarterly. If the future value of the annuity after 3 years is $40,000, what was the size of each payment? Round your answer to the nearest cent.

Find the present value of the ordinary annuity. Please round the answer to the nearest cent. $2,000 per semiannual period for 8 yr at 12%/year, compounded semi-annually P = $__________

Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. S = 110,000, r = 4.5, t = 22, m = 4

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. P = 23,000, r = 3, t = 12, m = 3

Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 10%/year compounded monthly. If the future value of the annuity after 10 years is $70,000, what was the size of each payment? Round your answer to the nearest cent.

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. P = 80,000, r = 9, t = 12, m = 2

Find the amount (future value) of the ordinary annuity. Please round the answer to the nearest cent. $200/month for yr at 7%/year, compounded monthly S = $ __________

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. P = 60,000, r = 10.5, t = 29, m = 10

Suppose payments will be made for years at the end of each semiannual period into an ordinary annuity earning interest at the rate of 8.5%/year compounded semiannually. If the present value of the annuity is $40,000, what should be the size of each payment? Round your answer to the nearest cent.

Quiz 5: Mathematics of Finance

Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​ P = 3,000, r = 5, t = 3, m = 4 ​

Determine whether the statement is true or false; explain why. ​ The present value of an annuity can be found by multiplying the future value by compound interest multiplier - .

Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​ S = 280,000, r = 11, t = 26, m = 13 ​

Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. Round your answer to the nearest cent. ​ S = 20,000, r = 4, t = 7, m = 4 ​