Question

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

Answer 1

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

Solution:-

Information given:-

• Principal amount = $6,746
• Rate of Interest = 5%
• Future amount = $1,000,000
• Time = ?

Calculation of compound interest

Rate = 5% / 4 = 1.25% (compounded quarterly)

Formula to calculate Number of years :

Amount Accrued = Principal amount * (1 + Rate / 100)^{number of years}

$1,000,000 = $6,746 * ( 1 + 1.25 / 100)^{number of years}

$1,000,000 / 6,746 = (1.0125)^{number of years}

$148.236 = (1.0125)^{number of years}

Introduction logarithms on both sides:

log148.236 = log(1.0125)^{number of years}

log148.236 = nlog(1.0125)

number of years = log148.236 / log(1.0125)

number of years = 402.398

But, 1 year = 4 quarters

Number of years = 402.398 / 4

Number of years = 100.6 or 101 years

I Hope I was able to help you. If this is helpful for you. Please give a THUMBS UP.

Thank you!!