Suppose a young couple deposits $1,100 at the end of each quarter in an account that earns an annual rate of 8.8%, compounded quarterly, for a period of 6 years. After the 6 years, they start a family and find they can contribute only $300 per quarter. If they leave the money from the first 6 years in the account and continue to contribute $300 at the end of each quarter for the next years, how much will they have in the account (to help with their child's college expenses)? Round your answer to the nearest cent.
A) $171,621.52
B) $226,229.22
C) $54,607.70
D) $280,836.92
E) $397,850.74

Question

Suppose a young couple deposits $1,100 at the end of each quarter in an account that earns an annual rate of 8.8%, compounded quarterly, for a period of 6 years. After the 6 years, they start a family and find they can contribute only $300 per quarter. If they leave the money from the first 6 years in the account and continue to contribute $300 at the end of each quarter for the next  years, how much will they have in the account (to help with their child's college expenses)? Round your answer to the nearest cent. ​
A) $171,621.52 
B) $226,229.22 
C) $54,607.70 
D) $280,836.92 
E) $397,850.74

Quizplus · Accepted Answer

Using the formula for compound interest, we can find that the amount in the account after the first 6 years is:

A = 1100(1 + 0.088/4)^(4*6) = $28,669.29

We can then use the formula for future value of an annuity to find the amount in the account after the next 11 years of quarterly deposits of $300:

FV = 300[((1 + 0.088/4)^(4*11) - 1)/(0.088/4)] = $28,150.93

Adding these two amounts gives the total value in the account after 17 years:

$28,669.29 + $28,150.93 = $56,820.22

Finally, we can use the formula for future value of a lump sum to find the value of this amount after the next 11 years of compound interest:

FV = $56,820.22(1 + 0.088/4)^(4*11) = $226,229.22

Therefore, the best choice is B, which is closest to our calculated answer.

Suppose a Young Couple Deposits $1,100 at the End of Each