Question

How long will it take for $4700 compounded semiannually at an annual rate of 1.5% to amount to $6200

Answer 1

Use the following formula for the amount of money obtained with a compounded interest:

`A=P(1+(r)/(n))^(nt)`

where,

A: amount earnt = 6200

P: principal = 4700

r: interest rate in decimal form = 0.015

n: times at year = 2 (semiannually)

Replace the previous values of the parameters into the formula for A, simplify and solve for t by using properties of logarithm, as follow:

`\begin{gathered} 6200=4700(1+(0.015)/(2))^(2t) \\ 6200=4700(1.0075)^(2t) \\ (6200)/(4700)=(1.0075)^(2t) \\ 1.3191=(1.0075)^(2t) \\ \log _(1.0075)(1.32)=2t \\ t=(1)/(2)\log _(1.0075)(1.32) \\ t=(1)/(2)\cdot(\log1.32)/(\log1.0075) \\ t\approx18.5349 \end{gathered}`

Hence, approximately 18.5349 years are necessary to obtain an amount of $6200