Question

Darain's grandson, Awan, is five years old today. Awan's parents, Maan and Jaba, have plans for Awan to attend a four-year university at age 18. Darain would like to save enough to pay for Awan's college tuition. Currently, tuition is $15,000 per year and is expected to increase at 7% per year. Darain can earn an annual compound investment return of 10%. Calculate how much Darain needs to start saving at the end of each year (beginning this year) to pay for Awan's college tuition. Assume Darain's last payment is made at the beginning of Awan's first year in college.

Answer 1

To pay for Awan's college tuition, Darain needs to start saving at the end of each year using compound interest. The present value of future tuition payments can be determined by calculating the future value of the tuition and saving that amount.

Step-by-step explanation:

To calculate how much Darain needs to save annually, we need to consider several factors:

Future cost of tuition:

Inflation: Tuition is expected to increase by 7% per year for 13 years (Awan's age difference: 18 - 5). We need to calculate the future cost of each year of tuition considering this inflation.

Total cost: Multiply the inflated cost of each year by the number of years (4) to get the total cost for the entire university education.

Present value:

Discount rate: Darain's investment return is 10%. We need to discount the future costs back to their present value to determine how much to save now.

Savings formula: Use the present value formula to calculate the annual savings required, considering the discounted future costs and the investment return.

Here's the calculation process:

Future cost of tuition:

Year 1: $15,000 × (1 + 0.07) = $16,050

Year 2: $16,050 × (1 + 0.07) = $17,154.05

Year 3: $17,154.05 × (1 + 0.07) = $18,325.24

Year 4: $18,325.24 × (1 + 0.07) = $19,565.70

Total cost:

4 years × ($16,050 + $17,154.05 + $18,325.24 + $19,565.70) = $71,095.19

Present value:

Discount rate: 10%

Future cost: $71,095.19

Using the present value formula (PV = FV / (1 + r)ⁿ):

PV = $71,095.19 / (1 + 0.10)¹³ ≈ $30,093.70

Therefore, Darain needs to save approximately $30,093.70 at the end of each year for 13 years to cover Awan's entire college tuition with his assumed investment return.

Answer 2

To pay for Awan's college tuition, Darain needs to start saving $304,073.01 at the end of each year.

Step-by-step explanation:

To calculate how much Darain needs to start saving at the end of each year in order to pay for Awan's college tuition, we can use the future value of an annuity formula. The formula for future value of an annuity is:

`FV = P * [(1 + r)^(n - 1)] / r`

Where:

• FV is the future value of the annuity
• P is the payment amount at the end of each year
• r is the interest rate per period (annual interest rate divided by the number of compounding periods per year)
• n is the number of compounding periods

In this case, Awan will attend college at age 18, which is a 13-year time period. The interest rate is 10% per year, and the tuition is currently $15,000 per year, increasing at 7% per year. So the calculation would be:

FV = $15,000 * [(1 + 0.10)^13 - 1] / 0.10 = $304,073.01

Therefore, Darain needs to start saving $304,073.01 at the end of each year to pay for Awan's college tuition.