Question

Imagine Homer Simpson actually invested $100,000 five years ago at
a 6.5 percent annual ineterest rate. If he invests an additional
$200 a month starting now for 20 years at the same 6.5 percent
annual rate, how much money will Homer have 20 years from now?

please please show work and show (a timeline of the answers,
this is important). handwritten if possible

Answer #1

FV of Amount Invested = Amount Invested five years ago * (1 +
r)^{(n + 5)}

= $100,000 * (1 + 0.065)^{(20 + 5)}

= $100,000 * 4.8277 = $482,769.91

FV of Annuity Due = Payment + Payment * [{1 - (1 +
r)^{-(n-1)}} / r]

= $200 + $200 * [{(1 + 0.065/12)^{[(20*12)-1]} - 1} /
(0.065/12)]

= $200 + $200 * [2.6367 / 0.0054]

= $200 + $200 * [486.7842]

= $200 + $97,356.84 = $97,556.84

Balance in Homer's Account 20 years from now = FV of Amount Invested + FV of Annuity Due

= $482,769.91 + $97,556.84 = $580,326.75

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