Question

# Derek will deposit \$3,997.00 per year for 13.00 years into an account that earns 12.00%. Assuming...

Derek will deposit \$3,997.00 per year for 13.00 years into an account that earns 12.00%. Assuming the first deposit is made 5.00 years from today, how much will be in the account 31.00 years from today? round 2 decimals

Value at year 4 = Annuity * [1 - 1 / (1 + r)^n] / r

Value at year 4 = 3997 * [1 - 1 / (1 + 0.12)^13] / 0.12

Value at year 4 = 3997 * [1 - 0.229174] / 0.12

Value at year 4 = 3997 * 6.423548

Value at year 4 = 25,674.92302

Value today = Future value / (1 + r)^n

Value today = 25,674.92302 / (1 + 0.12)^4

Value today = 25,674.92302 / 1.573519

Value today = 16,316.8774

Value in 31 years = Present value (1 + r)^n

Value in 31 years = 16,316.8774 (1 + 0.12)^31

Value in 31 years = 16,316.8774 * 33.555113

Value in 31 years = \$547,514.66

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