Answer to Question #171456 in Microeconomics for komal

Question

How long will it take a given sum of money (say in rupees) to increase 4 times its present value when compounded half year at 7% rate of interest?

Answer 1

A = the value of the accrued investment.

P = the principal amount.

R = the annual interest rate.

N = the number of times that interest is compounded per unit t.

T = the time the money is invested or borrowed for

A= 4, P=1, R= 0.07 N = 2

T =?

Find $\frac{R}{N} = \frac{0.07}{2} = 0.035$

Formula: $A = P [1+\frac{R}{N} ]^{N\times T}$

$4 = 1 [1+\frac{0.07}{2} ]^{2\times T}$

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

$(1.071225) ^{T} =4$

Take logarithms on both sides:

Tlog1.071225 = log4

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

$T = \frac{0.6020599913}{0.0298806996} = 20.15\; years$ = 20 years and 2 months

It will take approximately 20 years and 2 months for a given sum of money (say in rupees) to increase 4 times its present value