Question

TD Bank is offffering a savings account which earns an annual interest rate of 3.25%. If John wishes to double

his initial investment, how long will his money have to remain in the account with

a) Simple interest?

b) Interest compounded monthly?

Answer 1

Simple Interest

Annual interest rate = r = 3.25%

Let P is John's initial investment. For this amount to get doubled in n years, the interest earned over n years has to be equal to P.

The Formula to calculate interest is:

I = P.r.n

P = P*3.25%*n

Therefore, n = 1/3.25% = 100/3.25 = 30.77 years

Answer -> 30.77 years

Compound Interest

Compounded monthly, annual interest rate = 3.25%

Therefore, monthly interest rate = 3.25%/12 = 0.270833%

Amount = P*(1+(r/12))^12*n

2*P = P*(1+(3.25%/12))^12*n

2 = (1+(3.25%/12))^12*n

Taking log both the sides

ln(2) = 12*n*ln(1+(3.25/12))

n = 0.69314718/(12*0.00270467) = 21.3564737 years

Answer -> Simple interest - 30.77 years; Compounded Monthly - 21.36 years