Question

When Derrick turned 15, his grandparents put $10,000 into an account that yielded 4% interest, compounded quarterly. When Derrick turns 18, his grandparents will give him the money to use toward his college education. How much does Derrick receive from his grandparents on his 18th birthday?

Answer 1

Derrick will receive $11,268.25 from his grandparents on his 18th birthday, which is the amount of $10,000 principal growing at 4% interest compounded quarterly over 3 years.

Step-by-step explanation:

When Derrick turned 15, his grandparents deposited $10,000 into an account with a 4% interest rate, compounded quarterly. To calculate how much money Derrick will receive on his 18th birthday, we can use the formula for compound interest:

`A = P(1 + r/n)^(^n^t^)`

where:

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

In Derrick's case:

• P = $10,000
• r = 4/100 = 0.04 (since the rate is a percentage, we convert it to a decimal)
• n = 4 (interest is compounded quarterly)
• t = 18 - 15 = 3 years

So the formula becomes:

`A = 10000(1 + 0.04/4)^(^4^*^3^)`

Calculate the powers and the division inside the brackets, then multiply by the principal:

A = 10000(1 + 0.01)¹²

A = 10000(1.01)¹²

A = 10000(1.126825)

A = $11,268.25

Therefore, on his 18th birthday, Derrick will receive $11,268.25 from his grandparents.