Question

A person invests 6500 dollars in a bank. The bank pays 6.25% 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 9000 dollars?

Answer 1

Answer: 14.4

Explanation:

Answer 2

`5.3\ years`

Explanation:

we know that

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

`A=\$9,000\\ P=\$6,500\\ r=0.0625\\n=2`

substitute in the formula above and solve for t

`9,000=6,500(1+(0.0625)/(2))^(2t)`

`1.38462=(1.03125)^(2t)`

applying log both sides

`log(1.38462)=(2t)log(1.03125)`

`t=log(1.38462)/2log(1.03125)=5.3\ years`