Answer :
It will take 18 years to reach an amount of $ 27200
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = PRT / 100
where P = Principal
R = rate of interest
T = time period
Given data ,
The principal amount = $ 8400
Interest rate = 6.75 %
= 0.0675
Let the time period be = n
The Amount in n years = $ 27200
Now ,
The Amount is calculated by the formula ,
A = P ( R+1 )ⁿ
where n = time period
Substituting the values of A , P , and R , we get
27200 = 8400 x ( 1.0675 )ⁿ
Dividing by 8400 on both sides , we get
( 1.0675 )ⁿ = 68 / 21
Taking logarithm on both sides , we get
[tex]n=log_{1. 0625} \frac{68}{21}[/tex]
On solving the equation , we get
n ≈ 18 years
Hence , it will take 18 years to reach an account value of $ 27200
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