You are currently saving for your child's college education.The current cost of college is R10,000 a year.You expect that college costs will continue to increase at a rate of 5 percent a year.Your child is scheduled to begin attending a four-year college 10 years from now .You currently have R25,000 in an account which earns 6 percent after taxes.You would like to have all of the necessary savings by the time your child enters college, and you would like to contribute a constant amount at the beginning of each of the next 10 years in order to provide the necessary amount.(You want to make 10 equal contributions starting in Year 0 and ending at Year 9.) How much should you contribute to the account each year in order to fully provide for your child's education?

Question

Quizplus · Accepted Answer

First, we need to calculate the total cost of four-year college education for the child, which can be done as follows:

Total cost = cost per year * number of years * (1 + rate of increase) ^ number of years

Total cost = R10,000 * 4 * (1 + 0.05) ^ 4
Total cost = R10,000 * 4 * 1.2155
Total cost = R48,621.94

Next, we need to calculate the future value of the R25,000 in 10 years, which can be done using the compound interest formula:

Future value = present value * (1 + interest rate) ^ number of years

Future value = R25,000 * (1 + 0.06) ^ 10
Future value = R25,000 * 1.7908
Future value = R44,770.06

Now, we can calculate the amount we need to contribute each year using the annuity formula:

PMT = (future value * interest rate) / ((1 + interest rate) ^ number of years - 1)

PMT = (R48,621.94 - R44,770.06 * 0.06) / ((1 + 0.06) ^ 10 - 1)
PMT = R13,414.88 / 7.3601
PMT = R1,825.85

However, we need to make 10 equal contributions, so we divide this amount by 10:

PMT = R1,825.85 / 10
PMT = R1,393.42

Therefore, the amount we should contribute each year is R1,393.42. Choice B is the correct answer.

You Are Currently Saving for Your Child's College Education