Answer:
101 years
Step-by-step explanation:
From the question we are given;
- Amount deposited (principal) $6746
- Rate of interest 5%
- Amount accrued is $ 1,000,000
We are required for the amount invested to accrue to the amount given;
We are going to use the compound interest formula;
[tex]A = P (1 + \frac{R}{100})^n[/tex], Where A is the amount accrued, P is the principal amount, R is the rate of interest.
R = 5 ÷ 4
= 1.25 % ( compounded quarterly)
Therefore;
[tex]1000,000=6746(1+\frac{1.25}{100})^n[/tex]
[tex]148.236=(1.0125)^n[/tex]
Introducing logarithms on both sides
[tex]log148.236=log(1.0125)^n\\log148.236=nlog(1.0125)\\n=\frac{log148.236}{log(1.0125)} \\ = 402.398[/tex]
But, 1 year = 4 quarters
Therefore;
Number of years = 402.398 ÷ 4
=100.6 years
= 101 years
Thus, it will take approximately 101 years
