Question

How long would it take to triple your money if the interest rate was:

5% compounded yearly

5% compounded monthly

5% compounded weekly

5% compounded continuously

Answer 1

IF initial amount be M, then

M x FVIF(r%, N) = 3 x M

FVIF(r%, N) = 3

(1 + r)^N = 3

(1) 5% compounded yearly: r = 5% = 0.05

(1.05)^N = 3

Taking natural logarithm on each side,

N x ln 1.05 = ln 3

N x 0.0488 = 1.0986

N = 22.51 years

(2) 5% compounded monthly: r = 5%/12 = 0.4167%

(1.004167)^12N = 3

Taking natural logarithm on each side,

12N x ln 1.004167 = ln 3

12N x 0.0042 = 1.0986

N = 22.02 years

(3) 5% compounded monthly: r = 5%/52 = 0.0962%

(1.000962)^52N = 3

Taking natural logarithm on each side,

52N x ln 1.000962 = ln 3

52N x 0.0010 = 1.0986

N = 21.97 years

(4) With continuous compounding at 5%,

Future value = Present value x e^rN

3 x M = M x e^rN

e^rN = 3

Taking natural logarithm on each side,

rN x ln e = ln 3

rN = 1.0986 [Since ln e = 1]

0.05 x N = 1.0986

N = 21.97 years