Question

$6746 is deposited into a savings account at 5% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $1,000,000?

Answer 1

101 years

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;

`A = P (1 + (R)/(100))^n`, 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;

`1000,000=6746(1+(1.25)/(100))^n`

`148.236=(1.0125)^n`

Introducing logarithms on both sides

`log148.236=log(1.0125)^n\\log148.236=nlog(1.0125)\\n=(log148.236)/(log(1.0125)) \\ = 402.398`

But, 1 year = 4 quarters

Therefore;

Number of years = 402.398 ÷ 4

=100.6 years

= 101 years

Thus, it will take approximately 101 years