Question 1

Merrie borrowed $500 from her parents, agreeing to pay them back when she graduated from college in four years. If she paid interest compounded daily at 16%, how much would she owe at the end of the four years?

Accepted Answer

The correct answer is A.The amount of interest owed is $500 * (1 + 0.16/365)^365 * 4 - $500 = $448.02. The total amount owed is $500 + $448.02 = $948.02.

Question 2

What is the APY for 6% compounded continuously?

Accepted Answer

The formula for continuously compounded interest is A = Pe^(rt), where A is the ending balance, P is the principal, e is the mathematical constant approximately equal to 2.718, r is the annual interest rate, and t is the time period in years. To solve for the APY in this problem, we can use the formula APY = e^(r) - 1. Plugging in 6% for r, we get APY = e^(0.06) - 1 = 0.0618 or 6.18%. Therefore, the best choice is C.

Question 3

Merrie borrowed $1000 from her parents, agreeing to pay them back when she graduated from college in five years. If she paid interest compounded quarterly at 5%, how much would she owe at the end of the five years?

Accepted Answer

The amount owed can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($1000), r is the annual interest rate (5% or 0.05), n is the number of times that interest is compounded per year (quarterly, so 4 times), and t is the time the money is invested or borrowed for (5 years). Plugging in the values: A = 1000(1 + 0.05/4)^(4*5) = 1000(1 + 0.0125)^(20) ≈ $1282.

Question 4

You have $4300 that you invest at 5% simple interest. How long will it take for your balance to reach $7525?

Accepted Answer

The formula for simple interest is $I = P \times r \times t$, where $I$ is the interest earned, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Here, you want the total amount ($A$) to be $7525, where $A = P + I$, and you're given $P = $4300$ and $r = 5\% = 0.05$. The interest earned ($I$) would be $A - P = $7525 - $4300 = $3225$. Plugging into the formula, $3225 = 4300 \times 0.05 \times t$. Solving for $t$ gives $t = 3225 / (4300 \times 0.05) = 15$ years.

Question 5

What is the APY for 9.7% compounded annually?

Accepted Answer

APY stands for Annual Percentage Yield, which is the total amount of interest earned on an account in one year, including compound interest. Therefore, the APY for 9.7% compounded annually is simply 9.7%.

Question 6

What is the APY for 4% compounded continuously?

Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A is the amount at the end of the compounding period, P is the principal, e is Euler's number (approximately equal to 2.71828), r is the annual interest rate as a decimal, and t is the time in years. Solving for r in this formula gives r = ln(A/P)/t. Plugging in the given values, r = ln(1 + 0.04/1) = 0.0392. Converting to a percentage, the APY is 100*0.0392 = 3.92%. However, since the question asks for the nearest hundredth of a percent, we round up to 4.08%. Therefore, the best choice is B.

Question 7

What is the APY for 12.3% compounded weekly?

Accepted Answer

The Annual Percentage Yield (APY) can be calculated using the formula APY = (1 + r/n)^(n*1) - 1, where r is the annual interest rate (as a decimal), and n is the number of compounding periods per year. For a 12.3% interest rate compounded weekly, r = 0.123 and n = 52. Plugging these values into the formula gives APY = (1 + 0.123/52)^(52*1) - 1, which results in an APY of approximately 13.1%.

Question 8

What is the APY for 6.25% compounded daily?

Accepted Answer

The APY (Annual Percentage Yield) can be calculated using the formula APY = (1 + r/n)^(n*1) - 1, where r is the annual interest rate (as a decimal), and n is the number of compounding periods per year. For a 6.25% interest rate compounded daily, r = 0.0625, and n = 365. Plugging these values into the formula gives APY = (1 + 0.0625/365)^(365*1) - 1 ≈ 0.0645 or 6.45%.

Question 9

Juanita has $100 deducted from her paycheck at the end of each month and put into a savings account earning 11% interest compounded monthly. She continues these deposits for five years. How much is the account worth at the end of the five years?

Accepted Answer

The answer of Juanita has $100 deducted from her paycheck...

Question 10

What is the APY for 6% compounded weekly?

Accepted Answer

The APY (Annual Percentage Yield) can be calculated using the formula: APY = (1 + r/n)^(n*t) - 1, where r is the nominal rate (0.06), n is the number of compounding periods per year (52 for weekly), and t is the time in years (1 year). Plugging in the values, APY = (1 + 0.06/52)^(52*1) - 1 ≈ 6.18%.

Question 11

Suppose you invest in an account that pays 6% interest, compounded quarterly. You would like your investment to grow to $8000 in 14 years. How much would you have to invest in order for this to happen?

Accepted Answer

To find the initial investment, use the formula for compound interest: $ P = \frac{A}{(1 + \frac{r}{n})^{nt}} $, where $ A = 8000 $, $ r = 0.06 $, $ n = 4 $, and $ t = 14 $. Solving this gives approximately $3475.

Question 12

The Martin family has decided to save up for a new swimming pool. They want to save $14,000 in four years. They find a savings account for which interest was compounded monthly at 7.6%. How much will they have to deposit each month to meet this goal?

Accepted Answer

To find the monthly deposit, we use the future value of an annuity formula: FV = P * [(1 + r)^nt - 1] / r. Here, FV = $14,000, r = 0.076/12, n = 12, t = 4. Solving for P gives approximately $250.49.

Question 13

What is the APY for 9.6% compounded daily?

Accepted Answer

The APY (Annual Percentage Yield) can be calculated using the formula APY = (1 + r/n)^(n*1) - 1, where r is the annual interest rate (as a decimal), and n is the number of compounding periods per year. For a 9.6% interest rate compounded daily, r = 0.096, and n = 365. Plugging these values into the formula gives APY = (1 + 0.096/365)^(365*1) - 1 ≈ 0.10047, or 10.05%, which rounds to 10.1%.

Question 14

What is the APY for 10.2% compounded quarterly?

Accepted Answer

The APY (Annual Percentage Yield) can be calculated using the formula APY = (1 + r/n)^(n*1) - 1, where r is the annual interest rate (as a decimal), and n is the number of compounding periods per year. For 10.2% compounded quarterly, r = 0.102 and n = 4. Plugging these values into the formula gives APY = (1 + 0.102/4)^(4*1) - 1 = 1.025^4 - 1 ≈ 0.106, or 10.6%.

Question 15

Tara has $85 deducted from her paycheck at the end of each month and put into a savings account earning 9% interest compounded monthly. She continues these deposits for 10 years. Approximately how much is the account worth at the end of the 10 years?

Accepted Answer

The amount of money being added to the account each month is constant, so we can use the formula for the future value of an annuity:

FV = PMT * (((1 + r)^n - 1) / r)

Where FV is the future value, PMT is the payment each month, r is the monthly interest rate (9% / 12), and n is the number of months (10 years * 12 months/year = 120 months).

Plugging in the numbers, we get:

FV = 85 * (((1 + 0.09/12)^120 - 1) / (0.09/12)) = $16,450.07

Therefore, the best choice is C.

Question 16

What is the APY for 7.5% compounded quarterly?

Accepted Answer

The formula to calculate APY (Annual Percentage Yield) for quarterly compounded interest is:
APY = (1 + (interest rate/4))^4 - 1
Putting the values in the formula:
APY = (1 + (7.5%/4))^4 - 1
APY = 7.7%
Therefore, the correct option is (C) 7.7%.

Question 17

What is the APY for 5.3% compounded quarterly?

Accepted Answer

The APY (Annual Percentage Yield) can be calculated using the formula APY = (1 + r/n)^(n*1) - 1, where r is the annual interest rate (as a decimal), and n is the number of compounding periods per year. For 5.3% compounded quarterly, r = 0.053 and n = 4. Plugging these values into the formula gives APY = (1 + 0.053/4)^(4*1) - 1 ≈ 0.054, or 5.4%.

Question 18

A man cuts back on his latte habit and instead makes $20 deposits each month into a savings account earning 6% interest compounded monthly. He continues these deposits for eight years. How much will the account be worth after eight years?

Accepted Answer

The answer of A man cuts back on his latte...

Question 19

You have $7000 that you invest at 9% simple interest. What is the balance after 14 years?

Accepted Answer

Simple interest is calculated as Principal x Rate x Time. So, $7000 x 0.09 x 14 = $8,820 interest. Adding the principal, $7000 + $8,820 = $15,820.

Question 20

Suppose you invest in an account that pays 5% interest, compounded quarterly. You would like your investment to grow to $5000 in 16 years. How much would you have to invest in order for this to happen?

Accepted Answer

The correct answer is A.The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the annual interest rate, n is the number of times per year that the interest is compounded, and t is the number of years.In this case, we have A = $5000, r = 5%, n = 4 (since the interest is compounded quarterly), and t = 16. Substituting these values into the formula, we get:$5000 = P(1 + 0.05/4)^(4*16)$5000 = P(1.0125)^64$5000 = P(2.258)P = $5000/2.258P = $2258Therefore, you would have to invest $2258 in order for your investment to grow to $5000 in 16 years.

Quiz 21: Savings Models