An amount of $5,000 is invested on 2 December 2020 at 6% pa compounded quarterly. Calculate...

An amount of $5,000 is invested on 2 December 2020 at 6% pa compounded quarterly. Calculate the interest (I) earned between 2 December 2024 and 2 December 2027. Give your answer in dollars and cents to the nearest cent.

Expert Solution

Rate = 6% per annum

Rate per quarter = 1.5%

Value of investment on 2nd December 2024:

Total number of quarters between 2nd December 2020 and 2nd December 2024 = 4 years * 4 quarters per year = 16 quarters

Effective Annual Rate = 1.015 ^ (number of quarters) -1

= 1.015^16 -1 = 1.26898-1 = 26.898% (Effective annual rate is the rate which converts the compounded rate to annual interest rate)

Value of the investment on 2nd December 2024 = 5000 * (1.26898) = $6344.927738

Value of investment between 2nd December 2024 and 2nd December 2027:

Total number of quarters between above dates : 3*4 = 12 quarters

Effective Annual Rate = 1.015^12 -1 = 1.195618-1 = 19.5618%

Value of investment on 2nd December 2027

= 6344.927738*1.195618 =7586.1109

Interest earned between 2nd December 2027 and 2nd December 2024 =7586.1109 -6344.927738 = $1241.183162 Answer

Interest earned = $1241.183162

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jeff jeffy answered 1 year ago

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