Question

Bobby opened a bank account. He deposited $92.50 into his account every month for 10 months. He used $36.50 every month to pay for piano lessons. After 10 months, he used of the total money left in his account to go to a piano concert. What is the total amount of money Bobby spent to go to the concert?

Answer 1

To find out how much money Bobby needs to deposit in a bank account with 10% interest compounded annually to have $10,000 in ten years, the compound interest formula is used and adjusted to solve for the principal amount, yielding approximately $3,855.43.

Step-by-step explanation:

The question requires solving for the present value of a sum of money that grows with compound interest. First, we need to understand the formula for compound interest:
A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial sum of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

Step-by-Step:

1. Isolate the principal amount (P) in the compound interest formula:
   P = A / (1 + r/n)^(nt).
2. For this question, A = $10,000, r = 10% or 0.10, n = 1 (compounded annually), and t = 10 years.
3. Calculate the necessary initial deposit:
   P = $10,000 / (1 + 0.10/1)^(1*10) = $10,000 / (1.10)^10.
4. Compute the calculation to find P.
5. P ≈ $3,855.43, which is the amount Bobby needs to deposit into his bank account.