Question

A bank offers you 15% for 5 years. The first 3 years you deposit $8,826 at the end of each year, then no more after that. How much woold your account have at the end of the 5 years?

Answer 1

The total account balance after 5 years with a 15% annual compound interest rate can be calculated by finding the future value of each of the deposits made over the first three years. We use the formula for compounding interest to find the future values, then add them together to find the total balance.

Step-by-step explanation:

To determine how much an account would have at the end of 5 years with a 15% annual compound interest rate, we need to calculate the future value of the deposits made at the end of each of the first three years, while considering no additional deposits are made thereafter.

We use the future value formula for compound interest: FV = P(1 + r)^n, where P is the principal amount (initial deposit), r is the annual interest rate (in decimal form), and n is the number of years the money is invested.

For the first deposit of $8,826, there will be 5 compounding periods, so the future value will be $8,826(1 + 0.15)^5. For the second deposit also of $8,826, there will be 4 compounding periods, so its future value will be $8,826(1 + 0.15)^4. Lastly, the third deposit will have 3 compounding periods and its future value $8,826(1 + 0.15)^3.

We then sum these future values to get the total amount in the account after 5 years.