Answer to Question #135896 in Microeconomics for Mefi

Question

how long will it take a given sum of money to increase 4 times its present value when compounded half yearly at 7% rate of interest

Answer 1

solution

let the present value $P=1$ . Then the future value will be $A=4$

Since interest is compounded half yearly, $i=\frac{7\%}{2}=0.035$

$A=P*(1+i)^n$ $4=(1.035)^n$ $log (4)=n\ log (1.035)$

$n=\frac{log(4)}{log(1.035)} = 40.2976$

Since payments are made half yearly, the period it takes to grow an amount by a factor of 4 is

$=\frac{40.2976}{2}= 20.1488\ years$

answer: it will take 20.15 years