Question

Darla would like to collect $175,000 to buy a house in 12 years. She thinks she can save money in a money-market account earning 7% interest per year. She would like to deposit an amount Q today to open the account, make a deposit every year, and make the last deposit at the end of Year 12 into the account. She also believes that she can increase the value of the deposit that she makes into the account every year by 5% above what she deposited the previous year, starting with the amount Q. What is the value of Q with which she will have to open the account to make this happen?

$9,293

$9,350

$5,130

$6,677

Answer 1

Future value of deposits = 175000

Make deposit today to end of 12 years. so total number of deposit (n) =13

payment (P) = Q

interest rate (i) =7%

grwoth rate in deposit (g) =5%

As payment is increasing, we will calculate annuity by future value of growing annuity formula

Future value of growing annuity =first Annuity/(i-g)*(((1+i)^n)-((1+g)^n))

175000 = Q/(7%-5%)*(((1+7%)^13)-((1+5%)^13))

175000 = Q*26.20979289

Q = 175000/26.20979289

=6676.893661

So firsts paymetn Q is 6677