Question

Suppose you have $4400 deposited at 2.35% compounded semiannually. About long will it take yourbalance to increase to $6200?

Answer 1

Solution:

Given:

$\begin{gathered} P=\text{ \ }4400 \\ r=2.35\text{ \%}=\frac{2.35}{100}=0.0235 \\ n=2\text{ \lparen semi-annually\rparen} \\ A=\text{ \ }6200 \\ t=? \end{gathered}$

Using the compound interest formula;

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 6200=4400(1+\frac{0.0235}{2})^{2t} \\ \frac{6200}{4400}=(1+0.01175)^{2t} \\ 1.409=1.01175^{2t} \end{gathered}$

To get the time (t), we take the logarithm of both sides.

$\begin{gathered} log1.409=log1.01175^{2t} \\ \\ Applying\text{ the law of logarithm,} \\ log\text{ }a^x=xloga \\ \\ Thus; \\ log1.409=2t\times log1.01175 \\ \frac{log1.409}{log1.01175}=2t \\ 2t=29.3524 \\ t=\frac{29.3524}{2} \\ t=14.6762years \end{gathered}$

Therefore, the time it will take to increase the balance to $6200 is approximately 14.68 years.