Question

A person invests 3000 dollars in a bank. The bank pays 6.75% interest compounded

semi-annually. To the nearest tenth of a year, how long must the person leave the

money in the bank until it reaches 6700 dollars?

Answer 1

12.1 years

Explanation:

We are given that

Principal amount, P=$3000

Rate of interest, r=6.75% semi-annually

Amount, A=$6700

We know that

When r pays semi-annually

`A=P(1+(r)/(n* 100))^(nt)`

Where n=2

Using the formula

`6700=3000(1+(6.75)/(200))^(2t)`

`(6700)/(3000)=(1..03375)^(2t)`

`2.233=(1.03375)^(2t)`

Taking ln on both sides we get

`ln(2.233)=2t ln(1.03375)`

`2t=(ln(2.233))/(ln(1.03375))`

`t=(1)/(2)* (ln(2.233))/(ln(1.03375))`

`t=12.1 years`