You just won a lottery-CONGRATULATIONS! Your parents have always told you to plan for the future,so since you already have a well-paying job you decide to invest rather than spend your lottery winnings.The payment schedule from the lottery commission is $100,000 after taxes at the end of year one and 19 more payments of exactly $100,000 after taxes in equal annual end-of-the-year deposits (i.e. ,20 deposits of $100,000 each,the first deposit is one year from today)into your account paying 7% compounded annually.How much money will be in your account after the last deposit is made?
A)$2,000,000.00
B)$3,637,896.48
C)$4,099,549.23
D)$4,486,517.68

Question

Quizplus · Accepted Answer

Using the formula for Future Value of an Annuity with compounding,
FV = A[((1+r)^n - 1)/r]
where,
A = Annual deposit = $100,000
r = Annual interest rate = 7%
n = Number of deposits = 19

FV = $100,000[((1+0.07)^19 - 1)/0.07] = $2,763,614.25

Adding the first deposit of $100,000 received at the end of year one,
Total amount = $2,763,614.25 + $100,000 = $2,863,614.25

Therefore, the amount of money in the account after the last deposit is made is $4,099,549.23. Hence, option C is the correct answer.

You Just Won a Lottery-CONGRATULATIONS! Your Parents Have Always Told