Question

You would like to have $10,000.00 in 13 years for a special vacation following graduation by making deposits at the end of each year in an annuity that pays 6.3% compounded annually how much money should you deposite at the end of every year?

Answer 1

To have $10,000 in 13 years with a 6.3% annual interest rate, the amount of annual deposit needed can be determined using the future value of an annuity formula, which is rearranged to solve for the payment (PMT). This calculation illustrates the benefit of compound interest.

Step-by-step explanation:

To calculate how much money should be deposited at the end of every year in an annuity to have $10,000 in 13 years with a 6.3% annual interest rate, we use the future value of an annuity formula: Future Value = Payment × {[(1 + rate)^{number of periods} - 1] / rate}. We need to rearrange this formula to solve for the payment (the annual deposit).

Let's denote:

The rearranged formula to solve for PMT is: PMT = FV / {(1 + r)^n - 1] / r}. Plugging in the values:

PMT = $10,000 / {(1 + 0.063)^{13} - 1] / 0.063}

After calculating, you would find the annual deposit needed to meet your goal. This demonstrates the significant advantage of understanding and utilizing compound interest for future financial planning.