Question

Test Problems/Analytical Thinking Questions

1. Future value: Zainab Ali Yahya received a graduation present of $2,000 that she is planning on investing in a mutual fund that earns 8.5 percent each year. How much money will she have in three years?

2. Multiple compounding periods: Find the future value of a five-year $100,000 investment that pays 8.75 percent and that has the following compounding periods:

a. Quarterly.

b. Monthly.

c. Daily.

3. Present value: Husain Ahmed Abdulla is considering an investment that pays 7.6 percent, compounded annually. How much will he have to invest today so that the investment will be worth $25,000 in six years?

4. Present value: Your brother, Abdulrahman Ali Mohamed, has asked you for a loan and has promised to pay you $7,750 at the end of three years. If you normally invest to earn 6 percent per year, how much will you be willing to lend to your brother if you view this purely as a financial transaction (i.e. you don’t give your brother a special deal)?

5. Interest rate: You are in desperate need of cash and turn to your uncle, who has offered to lend you some money. You decide to borrow $1,300 and agree to pay back $1,500 in two years. Alternatively, you could borrow from your bank that is charging 6.5 percent interest annually. Should you go with your uncle or the bank?

6. Number of periods: You invest $150 in a mutual fund today that pays 9 percent interest annually. How long will it take to double your money?

Answer 1

1. Future Value

Where,
FV = Future Value
PV = Present Value
i = rate of return
n = number of years

given:
PV = $2000
i = 8.5% or 0.085
n = 3 years

Substituting the values in the formula, we get

2. Multiple compounding periods

A small modification to above formula;

Where,
FV = Future Value
PV = Present Value
i = rate of return
n = number of years
a = number of compounding in a year

a) Quarterly. (a = 4)

PV = $100,000
i = 8.75% or 0.0875
n = 5 years

So substituting the values in the formula, we get:

b) Monthly. (a = 12)

c) Daily. (a =365)

3. Present value:

FV = $25000
i = 7.6% or 0.076
n = 6 years

4. Present value:

Same formula as 3.

FV = 7750
i = 6% or 0.06
n = 3 years

Therefore, maximum amount willing to lend is $6,507.05

5. Interest rate:

Here,
FV = 1500
PV = 1300
n = 2 years
We need to find "i" that is interest, so that we can compare it with bank interest, and decide whether or not to borrow from uncle.

or

We can see that uncle is charging 7.42% and bank is charging 6.5%. So its not a good decision to borrow from uncle but go with bank.

6. Number of periods:

PV = 150
FV = 150 * 2 = 300
i = 9% or 0.09

..............(taking log₁₀ on both sides)

So it will take 8.04 years for the money to double at 9% interest paid annually.

There is an easy way to find out this, called 72 rule. Whenever you have interest rate and you need to know how many years it will take for your money to double, just divide 72 by interest rate.

n = 72 / 9
= 8 years.