Question

Can you please explain me this question? Thanks!

Anette made deposits of $2000 at the beginning of every three months for seven years into an investment fund that was earning 7.2% compounded quarterly. She left the money in the fund for another three years to accumulate interest. If the fund was earning the same interest rate during the entire time period, what was the amount of interest earned on her investment during the term?

Answer 1

FV of Annuity Due:
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.
FV of Annuity = (1+r) * CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

FV of Annuity Due after 7 years :

Particulars	Amount
Cash Flow	2000
Int Rate	1.800%
Periods	28

FV of Annuity Due = ( 1+ r) [ Cash Flow * [ [ ( 1 + r )^n ] - 1 ] /r ]
= ( 1 + 0.018 ) * [2000 * [ [(1+0.018)^28] - 1 ] / 0.018 ]
= ( 1.018 ) * [2000 * [ [( 1.018 ) ^ 28 ] - 1 ] / 0.018 ]
= ( 1.018 ) * [2000 * [ [ 1.6479 ] - 1 ] / 0.018 ]
= ( 1.018 ) * [ $ 71991.81 ]
= $ 73287.66

FV of $ 73287.66 after 3 years compounded quarterly

Particulars	Amount
Present Value	$    73,287.66
Int Rate	1.800%
Periods	12

Future Value = Present Value * ( 1 + r )^n

= $ 73287.66 ( 1 + 0.018) ^ 12

= $ 73287.66 ( 1.018 ^ 12)

= $ 73287.66 * 1.2387

= $ 90782.93

Tota amount of interest earned

= FV after 10 years - Investments made

= $ 90782.93 - $ 56000

= $ 34782.93

Pls do rate, if the answer is correct and comment, if any further assistance is required.