When Curtis was born, his parents began depositing $1000 at the end of every year into an annuity to save for his college education. If the account paid 7% compounded annually for the first 10 years and then dropped to 5% for the next eight years, how much is the account worth now that Curtis is 18 years old and ready for college?

Question

When Curtis was born, his parents began depositing $1000 at the end of every year into an annuity to save for his college education. If the account paid 7% compounded annually for the first 10 years and then dropped to 5% for the next eight years, how much is the account worth now that Curtis is 18 years old and ready for college?

Answer 1

To find the total worth of the account now, we need to calculate the accumulated value of the annuity for the first 10 years at a 7% interest rate, and then for the next 8 years at a 5% interest rate.

First, let's calculate the accumulated value for the first 10 years.

Step 1: Calculate the future value of each yearly deposit at 7% interest rate.
The future value of each yearly deposit can be calculated using the formula for the future value of an annuity:

Future Value = Payment * [(1 + Interest Rate)^(Number of Years) - 1] / Interest Rate

Future Value = $1000 * [(1 + 0.07)^10 - 1] / 0.07

Using a calculator, this calculates to approximately $12,875.60.

Step 2: Calculate the accumulated value for the first 10 years.
The accumulated value is the sum of the future values of each yearly deposit.

Accumulated Value = Future Value * (1 + Interest Rate)^(Number of Years)

Accumulated Value = $12,875.60 * (1 + 0.07)^10

Using a calculator, this calculates to approximately $23,355.76.

Now, let's calculate the accumulated value for the next 8 years at a 5% interest rate.

Step 3: Calculate the future value of each yearly deposit at 5% interest rate.
Using the same formula as earlier, but with a 5% interest rate:

Future Value = $1000 * [(1 + 0.05)^8 - 1] / 0.05

Using a calculator, this calculates to approximately $9,323.08.

Step 4: Calculate the accumulated value for the next 8 years.
Again, using the same formula as earlier:

Accumulated Value = Future Value * (1 + Interest Rate)^(Number of Years)

Accumulated Value = $9,323.08 * (1 + 0.05)^8

Using a calculator, this calculates to approximately $13,562.17.

Finally, let's calculate the total worth of the account now by summing up the accumulated values for both periods:

Total Worth = Accumulated Value for the first 10 years + Accumulated Value for the next 8 years

Total Worth = $23,355.76 + $13,562.17

The total worth of the account now is approximately $36,917.93.