Answer to Question #178014 in Microeconomics for Ratna

Question #178014

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?


1
Expert's answer
2021-04-16T12:41:06-0400

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.


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