MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

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,[tex]A=P(1+r)^t[/tex]Where, A is the amount A=$1950P is the principal P=$1700r is the interest rate r=6.88%=0.0688t is the time Substitute the values in the formula,[tex]1950=1700(1+0.0688)^t[/tex][tex]\frac{1950}{1700}=(1.0688)^t[/tex][tex]1.147=(1.0688)^t[/tex]Taking log both side,[tex]\log(1.147)=\log ((1.0688)^t)[/tex]Applying logarithmic formula, [tex]\log a^x=x\log a[/tex][tex]\log(1.147)=t\log (1.0688)[/tex][tex]t=\frac{\log(1.147)}{\log (1.0688)}[/tex][tex]t=2.06[/tex]Approximately, He invest for 2 years.