Question

Dylan is going to invest $360 and leave it in an account for 5 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest hundredth of a percent, would be required in order for Dylan to end up with $420?

Answer 1

The rate of interest at which Dylan invested is 3.09%.

The practice of adding interest to the principal of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. It happens when interest is reinvested, added to the collateral for the loan rather than paid out, or when the borrower is forced to pay it, resulting in interest being created on the principal amount plus any accumulated interest the following period. Compound interest is a prominent concept in finance and economics.

Compound interest allows interest to accumulate over time, in contrast to simple interest, which does not compound because past interest is not returned to the principle for the present period.

principal =360

time =5 years

n=5×4=20 (compounded quarterly)

Amount = 420

Now: 420 = 360(1+r)²⁰

solving for r we get:

r= 0.007737

required rate percent = 0.007737×4 = 0.00193 × 100 = 3.09%

hence the simple annual interest rate is obtained by multiplying the interest per period by the total number of periods in a year is 3.09%.

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