Question

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

Answer 1

Answer:

12.1 years

Step-by-step 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

$A=P(1+\frac{r}{n\times 100})^{nt}$

Where n=2

Using the formula

$6700=3000(1+\frac{6.75}{200})^{2t}$

$\frac{6700}{3000}=(1..03375)^{2t}$

$2.233=(1.03375)^{2t}$

Taking ln on both sides we get

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

$2t=\frac{ln(2.233)}{ln(1.03375)}$

$t=\frac{1}{2}\times \frac{ln(2.233)}{ln(1.03375)}$

$t=12.1 years$