Question 1

The amount to be invested today at a given interest rate over a specified period in order to equal a future amount is called

Accepted Answer

The amount to be invested today to equal a future amount is called the present value. The other options, Present Value Interest Factor (A) and Future Value Interest Factor (D), refer to numerical factors used in calculating present and future values, respectively. Future Value (B) refers to the value of an investment at a future point in time.

Question 2

If you want to have $10 000 for a down payment on a new car in three years, assuming an interest rate of 4.5 percent compounded annually, how much money do you need to deposit as a lump sum today?

Accepted Answer

The answer of If you want to have $10 000...

Question 3

What is the present value of $1000 to be received ten years from today, assuming an interest rate of nine percent per annum?

Accepted Answer

Using the formula for present value: PV = FV / (1+r)^n, where PV is present value, FV is future value, r is the interest rate and n is the number of years. Plugging in the given values, we get PV = $1000 / (1+0.09)^10 = $422. Therefore, D is the correct answer.

Question 4

Julian wants to figure out how more it will cost monthly to pay off his student loans if he borrows an extra $4000 a year for four years. This will allow him to rent a nicer place and take a holiday each year. Assume that no interest accrues until he completes his education and begins paying off the loan. The interest rate for the loan amount will be seven percent per year compounded monthly and he will pay it off over five years. What would his additional monthly payment be?

Accepted Answer

The answer of Julian wants to figure out how more...

Question 5

Betty wants to accumulate $1 million by the end of 20 years by making equal annual year-end deposits over the next 20 years. Assuming Betty can earn 10 percent over this period, how much must she deposit at the end of each year?

Accepted Answer

To find the annual deposit, we use the future value of an annuity formula: FV = Pmt * [(1 + r)^n - 1] / r. Here, FV = $1,000,000, r = 0.10, and n = 20. Solving for Pmt gives approximately $17,460.

Question 6

The future value of $810 received today and deposited at 7.71 percent compounded annually for four years is closest to

Accepted Answer

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Question 7

If you want to save $40 000 for a down payment on a home in five years, assuming an interest rate of 4.5 percent compounded annually, how much money do you need to save each month?

Accepted Answer

The answer of If you want to save $40 000...

Question 8

Hazel needs to plan how large a mortgage she can afford. How much would she need to pay monthly on a mortgage of $200 000 at six percent interest, calculated semi-annually and amortized over 30 years?

Accepted Answer

The answer of Hazel needs to plan how large a...

Question 9

The future value interest factor is

Accepted Answer

The future value interest factor (FVIF) is a multiplier used to calculate the future value of a present sum of money. It is always greater than 1.0 as it represents the growth rate of the investment over time. A value of 1.0 indicates no growth or interest, while values greater than 1.0 indicate growth and compounding interest.

Question 10

If the interest rate is zero, the future value interest factor equals

Accepted Answer

The future value interest factor (FVIF) is used to calculate the future value of a present sum of money with compound interest. When the interest rate is zero, the formula for calculating FVIF becomes (1 + 0)^n, which simplifies to 1^n, which equals 1. Therefore, the FVIF when the interest rate is zero is always 1.

Question 11

How long will it take Ivy's money to triple in value at 12 percent compounded quarterly?

Accepted Answer

The answer of How long will it take Ivy's money...

Question 12

In a recessionary economy, interest rate on deposits can be 0 percent. However, Raymond has an investment of $25 000 now, and in three years it will mature and pay Raymond $32 000. What is the approximate rate of return on his investment?

Accepted Answer

To calculate the rate of return on an investment, we can use the formula:

Rate of return = (final value - initial value) / initial value * 100

In this case, the initial value is $25 000 and the final value is $32 000, so:

Rate of return = (32 000 - 25 000) / 25 000 * 100
Rate of return = 7/25 * 100
Rate of return = 28%

Therefore, the approximate rate of return on Raymond's investment is 28%, which is closest to option B)8)6 percent.

Question 13

Raymond wants to save the college tuition fees he will need in ten years by starting with a deposit of $6500 today and depositing another $500 at the end of each year. How much will Raymond have in ten years if he gets a rate of return of four percent?

Accepted Answer

The answer of Raymond wants to save the college tuition...

Question 14

What is the present value of an ordinary annuity of $1550 each year for 15 years, with an interest rate of 6.6 percent per annum?

Accepted Answer

We can use the formula for the present value of an ordinary annuity:

PV = PMT x ((1 - (1 + r)^-n) / r)

where PV is the present value, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.

Plugging in the given values, we get:

PV = 1550 x ((1 - (1 + 0.066)^-15) / 0.066)
PV = $14,481.15

Therefore, the present value of the annuity is $14,481.15. Choice C is the correct answer.

Question 15

The future value of today's $200 to be received 10 years later with an interest rate of 10 percent per annum is

Accepted Answer

The answer of The future value of today's $200 to...

Question 16

Rebeccah is 65 and planing to retire next month. She can select a pension of $1745 monthly guaranteed for the rest of her life, but not indexed for inflation, or take a lump sum of $312 000. Assume she can invest the lump sum at five percent annually and draw the same income as the pension. How long does she need to live in order for the monthly pension to be the better choice?

Accepted Answer

To determine which option is better, we need to calculate the present value of the pension and compare it to the lump sum.

First, we calculate the present value of the pension using the formula for a level payment annuity:

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

Where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of payments.

PV = 1745 * (1 - (1 + 0.05/12)^-(12*20)) / (0.05/12) = $235,650.47

Therefore, the lump sum option is better if its present value is greater than $235,650.47.

PV of lump sum = $312,000

Since the lump sum option has a greater present value, it is the better choice unless Rebeccah expects to live longer than the break-even point. To calculate the break-even point, we need to find the number of months it takes for the present value of the pension to exceed $312,000.

PV of pension after k months = 1745 * (1 - (1 + 0.05/12)^-(12*k)) / (0.05/12)

Solving for k:

PV of pension after k months = 312,000

1745 * (1 - (1 + 0.05/12)^-(12*k)) / (0.05/12) = 312,000

1 - (1 + 0.05/12)^-(12*k) = 178.680017

(1 + 0.05/12)^-(12*k) = -177.680017

12*k = log(-177.680017) / log(1 + 0.05/12) = 155.338797

k = 12.9449

Therefore, the break-even point is 12.9449 months or approximately 92 months (since Rebeccah cannot live a fraction of a month). If Rebeccah expects to live longer than 92 months, then the pension option is better. Otherwise, the lump sum option is better.

So, the best choice for Rebeccah depends on her life expectancy and personal financial goals.

Question 17

Danny invests $124 090 in a fund and expects to receive $10 000 per year for the next 30 years. What is the approximate rate of return?

Accepted Answer

The approximate rate of return can be calculated using the formula for the present value of an annuity. Solving for the interest rate that equates the present value of $10,000 per year for 30 years to $124,090 gives a rate close to 7 percent.

Question 18

The future value of $676 received today and deposited at 5.85 percent compounded annually for five years is closest to

Accepted Answer

The answer of The future value of $676 received today...

Question 19

Aleem needs to figure out how much interest he would save if he paid off his mortgage over 15 years instead of 30 years? His mortgage is $100 000 at six percent interest calculated semi-annually.

Accepted Answer

The answer of Aleem needs to figure out how much...

Question 20

If you borrow $20 000 as a five-year loan from the bank and the bank requires you to make end-of-year payments of $4878.05, what is the annual interest rate on this loan?

Accepted Answer

We can use the formula for present value of an annuity to solve for the interest rate.
PV = PMT x (1 - (1 + r)^-n) / r
where PV = present value of loan ($20 000), PMT = payment per year ($4878.05), r = annual interest rate, and n = number of years (5).

Substituting the given values:
$20 000 = $4878.05 x (1 - (1 + r)^-5) / r

Using trial and error, we can find that the annual interest rate that satisfies this equation is approximately 7 percent. Therefore, the best choice is C.

Quiz 2: Tools for Financial Planning - Applying Time Value Concepts