Question 1

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 2

Nick invests $50 000 today and the fund guarantees an 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. By solving for the interest rate that equates the present value of the annuity payments ($12,345 for 6 years) to the initial investment ($50,000), the approximate rate of return is found to be 12.5 percent.

Question 3

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?

Accepted Answer

The present value of an ordinary annuity formula is:
PV = A x ((1 - (1+r)^-n)/r)
where PV is the present value of the annuity, A is the annual payment, r is the interest rate per period, and n is the number of periods.
Plugging in the values from the problem, we get:
PV = 1550 x ((1 - (1+0.066)^-15)/0.066)
PV = 1550 x ((1 - 0.2424)/0.066)
PV = 1550 x (11.5081)
PV = $14,480.62
Therefore, the present value of the annuity is $14,480.62, so answer choice C is correct.

Question 4

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

Accepted Answer

The answer of The future value of $810 deposited today...

Question 5

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

To find the annual interest rate on the loan, we need to use the formula for calculating the present value of an annuity:

PV = C x [(1 - (1 / (1 + r)^n)) / r]

where:
PV = present value of the annuity (in this case, the $20,000 loan)
C = annual end-of-year payment
r = annual interest rate
n = number of years

Plugging in the given values, we get:

$20,000 = $4,878.05 x [(1 - (1 / (1 + r)^5)) / r]

Simplifying this equation using algebra, we get:

r = 7 percent

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

Question 6

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 7

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

To calculate the present value, we use the formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years. Plugging in the numbers, we get PV = 1000 / (1 + 0.09)^10 = $422. Therefore, the best choice is D.

Question 8

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 9

In a recessionary economy,the 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 annual interest rate he will receive?

Accepted Answer

To find the annual interest rate, we can use the formula:

future value = present value * (1 + interest rate)^time

Plugging in the values given in the problem, we get:

$32,000 = $25,000 * (1 + interest rate)^3

Simplifying, we get:

1.28 = (1 + interest rate)^3

Taking the cube root of both sides, we get:

1.089 = 1 + interest rate

Subtracting 1 from both sides, we get:

interest rate = 0.089 or 8.9%

Therefore, the approximate annual interest rate Raymond will receive is 8.6% (rounded to one decimal place).

Question 10

Assuming an inflationary economy,the future value interest factor is

Accepted Answer

In an inflationary economy, the value of money decreases over time, so the future value of a sum of money will be greater than the present value. Therefore, the future value interest factor will always be greater than 1.0.

Question 11

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

Accepted Answer

We can use the formula A = P(1 + r/n)^(nt), where A is the ending amount, P is the principal (starting amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded in a year, and t is the number of years. We want to solve for t when A/P = 3 and r = 0.12/4 (since it's compounded quarterly). Plugging in the values, we get:

3 = (1 + 0.12/4)^(4t)
ln(3) = 4t * ln(1 + 0.12/4)
t = ln(3)/(4 * ln(1 + 0.12/4)) ≈ 9.3 years

Therefore, the answer is C) 9)3 years.

Question 12

Hazel needs to plan the mortgage amount 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 correct answer is D because the monthly payment on a mortgage of $200,000 at six percent interest, calculated semi-annually and amortized over 30 years is $1190.

Question 13

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

Accepted Answer

The answer of The future value of $676 deposited at...

Question 14

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

Accepted Answer

The interest rate 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 approximately 7 percent.

Question 15

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

To calculate the annual rate of return, we can use the compound interest formula: 
Future value = Present value x (1 + r)^n 
where r is the annual rate of return, n is the number of years, and we want to solve for r. 
In this case, we know the present value (PV) is $2, the future value (FV) is $600, and n is 50 years.

$600 = $2 x (1 + r)^50 
Dividing both sides by $2: 
$300 = (1 + r)^50

To approximate the annual rate of return, we can take the 50th root of both sides: 
(1 + r) ≈ 1.12

Subtracting 1 from both sides: 
r ≈ 0.12 or 12%

Therefore, the correct answer is B) 12 percent

Question 16

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 in order to equal a future amount is called present value. The other options, present value interest factor and future value interest factor, refer to mathematical formulas used to calculate present value and future value. Future value refers to the value of an investment after a specified period at a given interest rate.

Question 17

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?

Accepted Answer

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

Question 18

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

The answer of Betty wants to accumulate $1 million by...

Question 19

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

Accepted Answer

When the interest rate is zero, there is no interest to be accrued, and the future value of any investment remains the same as its present value. Therefore, the future value interest factor would be 1.0.

Question 20

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?

Accepted Answer

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

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