Question

1. What nominal rate compounded annually would quadruple the principal in 4
years?
2. A master card compounds monthly and charges an interest of 1.5% per month.
What is the effective interest rate per year?
3. How long will it take money to triple itself if invested at 8% compounded
annually?
4. Microsoft CEO, billionaire Bill Gates willed that a sum of $25 million be given to a
child but will be held in trust by the child’s mother until it amounts to $45 million. If
the amount is invested and earns 8% compounded quarterly, when will the child
receive the money?
5. A credit plan charges interest rate of 36% compounded monthly. Find its effective
rate.
6. Find the amount at the end of two years and seven months if P1000 is invested
at 8% compounded quarterly using simple interest for anytime less than a year
interest period.
7. A P2000 loan was originally made at 8% simple interest for 4 years. At the end of
this period the loan was extended for 3 years without the interest being paid, but
the new interest rate was made 10% compounded semiannually. How much
should the borrower pay at the end of 7 years?

Answer 1

1) Let interest rate be "r" compounded annually

4P = P * (1 + r)^⁴

4 = (1 + r)^⁴

Taking (1/4) of the root on both sides:

1 + r = 1.4142

r = 0.4142 which is 41.42%

2) Interest rate = 1.5% per month

Annual effective rate of interest: [1 + Monthly rate of Interest]^^{Number of compounding done in an year} = [1 + 0.015]^¹² = 1.1956 which is 19.56%

3) Let interest rate be "r" compounded annually

3P = P * (1 + r)^³

3 = (1 + r)^³

Taking (1/3) of the root on both sides:

1 + r = 1.4422

r = 0.4422 which is 44.22%

4) Interest rate = 8% compounded quarterly which means annual effective rate of interest is [1 + (8% / 2)]^⁴ = 1.0824 which is 8.24%

Amount Invested = 25 million

45 = 25 * 1.0824^ⁿ where "n" is number of years after which child recieve the money

n = 7.42 years