Question
Betty DeRose is going to deposit $2,800 into a savings account at
the beginning of every six months for the next ten years. Assume
the account will earn 20% interest compounded semi-annually.

Calculate the amount of interest Betty DeRose will earn over the
ten year period.
No credit will be awarded for this question using a means
other than these table factors to answer this question.

Future Value of an Annuity 5% 6% Rate of interest per period in percent Periods 72% 3% 5% 8% 9% 10% 12% 15% 20% 3 3.0150 3.09

Future Value of a Lump-Sum 15% 1.5209 1.7490 2.0114 20% 1.7280 2.0736 2.4883 Cauw Periods 2% 3 1.0151 | 1.0202 1.0253 1.0304

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Answer #1

Calculation of Future value of Annuity Due:

Since the annuity payments are starting at the beginning of the period, the annuity due/immediate is to be considered.

Future value of Annuity Due = (1+r)*P[((1+r)^n-1)/r]

Where r = rate per period =20% (In given case)

P = periodic payment = $ 2800

n = Number of periods = 10 years*2 = 20 periods

Future value of Annuity due=(1+0.20)*2800[((1+0.20)^20-1)/0.20]

= 1.20*2800(186.688) (As per Future value of Annuity table@20%,20 periods)

= $ 627271.68

Principal amount = $2800* 20 periods = $ 56000

Amount of interest = $ 627271.68- $ 56000 = $ 571271.68

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