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

Answer:

He invest for 2 years.

Step-by-step 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,

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

$\frac{1950}{1700}=(1.0688)^t$

$1.147=(1.0688)^t$

Taking log both side,

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

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

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

$t=\frac{\log(1.147)}{\log (1.0688)}$

$t=2.06$

Approximately, He invest for 2 years.