Question

A person invests 200,000 into a saving account yielding 8% per annum compounded monthly. After 2 years
the interest rate is raised to 12% p.a. compounded quarterly and further 11⁄2 year later the interest rate raised to
16% compounded semi-annually.
(a) How much interest the person would earn, if he keeps his money in the account for a total of six years?
(b) What was the effective rate of interest received by the person during the final year of his investments?

Answer 1

Answer:

  (a)  211,555.72

  (b)  16.64%

Step-by-step explanation:

You want to know the total interest earned on a 200,000 investment at ...

• 8% compounded monthly for 2 years
• 12% compounded quarterly for 1.5 years
• 16% compounded semiannually for 2.5 years

And you want to know the effective rate for the last period.

Multiplier

The multiplier of the investment at rate r compounded n times per year for t years is ...

  k = (1 +r/n)^(nt)

Application

Using this multiplier for the rates and periods given the balance of the account at the end of 6 years will be ...

  200,000(1 +.08/12)^(12·2) × (1 +.12/4)^(4·1.5) × (1 +.16/2)^(2·2.5)

  ≈ 411,555.72

(a) Interest

The interest earned is the difference between the account balance and the principal invested:

  411,555.72 -200,000 = 211,555.72 . . . . interest earned in 6 years

(b) Effective rate

The annual multiplier for the last term is ...

  (1 +.16/2)^(2·1) = 1.1664

The effective interest rate is 1 less than this:

  16.64% = effective rate during final year

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Additional comment

The repetitive math can be less tedious if you let a calculator or spreadsheet do it.

No currency units are given in the problem statement.