Question

Suppose you plan to go on a dream vacation for your anniversary 10 years from today, and you plan to save up $5,368 for the trip. If your bank is offering a 5% APR interest on deposits, you can calculate how much you need to deposit today to reach your savings goal. By using the time value of money concept and the formula for future value of a deposit, you can determine the initial deposit amount required to achieve your savings target in 10 years.

Answer 1

To reach $10,000 in 10 years with a 10% annual interest rate, you should deposit approximately $3,855.43 today.

Step-by-step explanation:

To calculate the initial deposit required to achieve a savings goal with compound interest, one can apply a financial formula that involves the future value, the annual interest rate, and the number of compounding periods.

To reach $10,000 in 10 years with an interest rate of 10% compounded annually, you need to know how much to deposit today. Using the formula for the future value of a lump sum, P = F / (1 + r)^n, where P is the present value (or initial deposit), F is the future value, r is the annual interest rate expressed as a decimal, and n is the number of compounding periods.

Substituting the values: P = $10,000 / (1 + 0.10)^10, which simplifies to P = $10,000 / (1.10)^10, resulting in P ≈ $3,855.43. Therefore, an initial deposit of $3,855.43 is needed today to accumulate $10,000 in 10 years at a 10% annual interest rate.