Question 1

Hazel needs to plan the mortgage amount she can afford.How much would she need to pay at the end of each month on a mortgage of $200000 at six percent interest,calculated semi-annually and amortized over 30 years?

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Question 2

Raymond wants to save the college tuition fees his child 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?

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Question 3

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

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Question 4

Nick invests $50 000 today and the fund guarantees an ordinary annuity of $12 345 for six years.What is the approximate rate of return?

Accepted Answer

The rate of return can be calculated using the present value of an annuity formula. Given the present value ($50,000), the annuity payment ($12,345), and the number of periods (6 years), the approximate rate of return is 12.5 percent.

Question 5

Raymond has an investment of $25 000 now,and in three years it will mature and pay Raymond $32 000.What is the approximate annual interest rate he will receive?

Accepted Answer

The future value formula for compound interest is used: $FV = PV(1 + r)^n$. Here, $FV = 32000$, $PV = 25000$, and $n = 3$. Solving for $r$, we get approximately 8.6%.

Question 6

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

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Question 7

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

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Question 8

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

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Question 9

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

Accepted Answer

The amount to be invested today to equal a future amount is called the present value. Choices A and D refer to interest factors, which are calculations used to determine the present or future value of an investment based on interest rates and time periods. Choice B refers to the future amount itself, not the amount needed to invest today to reach that future amount.

Question 10

Danny invests $124 090 in a fund and expects to receive $10 000 per year,at the end of each year,for the next 30 years.What is the approximate interest rate provided on the annuity?

Accepted Answer

The interest rate can be found using the formula for the present value of an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value ($124,090), PMT is the annual payment ($10,000), n is the number of periods (30 years), and r is the interest rate per period. By plugging the values into the formula and solving for r, or by using a financial calculator or spreadsheet, we find that the interest rate that closely matches the given conditions is approximately 7 percent.

Question 11

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

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Question 12

If John makes annual year-end payments of $8337.83 on a 20-year loan with an annual interest rate of 7.5 percent,what is the original principal amount for John's loan?

Accepted Answer

The original principal amount of John's loan can be calculated using the formula for the present value of an annuity: $P = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where P is the principal, PMT is the annual payment, r is the annual interest rate (as a decimal), and n is the number of payments. Substituting the given values: $P = 8337.83 \times \left(\frac{1 - (1 + 0.075)^{-20}}{0.075}\right)$, we find that P is approximately $85,000, making option D the correct answer.

Question 13

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

Accepted Answer

When the interest rate is zero, there is no growth or change in the value of the money over time. Therefore, the future value interest factor will be 1.0, as there is no additional growth factor to be considered.

Question 14

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

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Question 15

Assuming an inflationary economy,the future value interest factor is

Accepted Answer

In an inflationary economy, the value of money decreases over time, meaning that the future value of money will be greater than its present value. Therefore, the future value interest factor (FVIF) will always be greater than 1.0, as it reflects the factor by which a present value will be multiplied to reach its future value.

Question 16

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

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Question 17

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 at the end of each month?

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Question 18

An antique was originally purchased 50 years ago for $2 and today is worth $600.What is the approximate annual rate of return realized on the sale of this antique?

Accepted Answer

The formula for annual rate of return is ((Current value / Original value)^(1/number of years)) - 1. Plugging in the values, we get ((600/2)^(1/50)) – 1, which simplifies to approximately 0.12 or 12%. Therefore, the annual rate of return realized on the sale of this antique is approximately 12%.

Question 19

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?

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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

Using the formula for the present value of an annuity:

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

where PV is the present value (the amount borrowed), PMT is the end-of-year payment, r is the annual interest rate, and n is the number of payments (in this case, 5).

Substituting the known values:

20000 = 4878.05 x (1 - 1/((1+r)^5))/r

Solving for r:

r = 0.07 or 7 percent

Therefore, the annual interest rate on this loan is 7 percent.

Quiz 1: Tools for Financial Planning - Applying Time Value Concepts