Question

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

Answer 1

Given:

`\begin{gathered} P=\text{ \$}4400 \\ r=2.35\text{ \%}=(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+(r)/(n))^(nt) \\ 6200=4400(1+(0.0235)/(2))^(2t) \\ (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* log1.01175 \\ (log1.409)/(log1.01175)=2t \\ 2t=29.3524 \\ t=(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.