Question

Suppose you have $1,950 in your savings account at the end of a certain period of time. You invested $1,700 at a 6.88% simple annual interest rate. How long, in years, did you invest your money? State your result to the nearest hundredth of a year.

Answer 1

He invest for 2 years.

Explanation:

Given : Suppose you have $1,950 in your savings account at the end of a certain period of time. You invested $1,700 at a 6.88% simple annual interest rate.

To find : How long, in years, did you invest your money?

Solution :

Applying simple interest formula,

`A=P(1+r)^t`

Where, A is the amount A=$1950

P is the principal P=$1700

r is the interest rate r=6.88%=0.0688

t is the time

Substitute the values in the formula,

`1950=1700(1+0.0688)^t`

`(1950)/(1700)=(1.0688)^t`

`1.147=(1.0688)^t`

Taking log both side,

`\log(1.147)=\log ((1.0688)^t)`

Applying logarithmic formula,
`\log a^x=x\log a`

`\log(1.147)=t\log (1.0688)`

`t=(\log(1.147))/(\log (1.0688))`

`t=2.06`

Approximately, He invest for 2 years.