Answer to Question #178014 in Microeconomics for Ratna

Question

How long will it take a given sum of money (Say in Rupees) to increase 4 times its present 

value when compounded half yearly at 7% rate of interest?

Answer 1

Solution:

Formula: $A = P [1+i ]^{N\times T}$

Where:

A= 4, P=1, i= 0.035 N = 2

T =?

Find $i = \frac{0.07}{2} = 0.035$

Insert the figures into the formula:

$4 = 1 [1+0.035]^{2\times T}$

$[1+0.035]^{2\times T} =4$

$[1.035]^{2\times T} =4$

$(1.071225) ^{T} =4$

Use logarithms on both sides:

Tlog1.071225 = log4

$T = \frac{log4}{log1.071225}$

$T = 20.14\; years$ = 20 years and 1.5 months

It will take approximately 20 years and one and a half months for a given sum of money to increase 4 times its present value when compounded half yearly when compounded half yearly at 7% interest rate.