Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's university education. They decide to make deposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 7%. The parents deposit $2 000 on their daughter's first birthday and plan to increase the size of their deposits by 5% each year. Assuming that the parents have already made the deposit for their daughter's 18th birthday, then the amount available for the daughter's university expenses on her 18th birthday is closest to:

Question

Quizplus · Accepted Answer

The question involves the calculation of the future value of an annuity. The formula for the future value of an annuity is as follows:

FV = Pmt x [(1 + r)^n - 1] / r

where FV is the future value of the annuity, Pmt is the periodic payment, r is the interest rate, and n is the number of periods.

In this case, the periodic payment is initially $2,000 and increases by 5% each year. The interest rate is 7%. The number of periods is 18. Using the formula above, we get:

FV = $2,000 x [(1 + 0.07)^18 - 1] / 0.07 x (1 + 0.05)

FV = $2,000 x 46.0056 x 1.05

FV = $97,331.20

Therefore, the amount available for the daughter's university expenses on her 18th birthday is closest to $97,331, which is answer choice C.

Suppose That a Young Couple Has Just Had Their First