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