Question

$800 is deposited in an account

that pays 9% annual interest,
compounded annually. Find the
balance after four years.

Answer 1

The balance after four years is $1129.27

Explanation:

The formula for compound interest, including principal sum, is
`A=P(1+(r)/(n))^(nt)`

• A = the future value of the investment/loan, including interest
• P = the principal investment amount (the initial deposit or loan amount)
• r = the annual interest rate (decimal)
• n = the number of times that interest is compounded per unit t
• t = the time the money is invested or borrowed for

∵ $800 is deposited in an account

∴ P = 800

∵ The account pays 9% annual interest

∴ r = 9% = 9 ÷ 100 = 0.09

∵ The interest is compounded annually

∴ n = 1

∵ The time is 4 years

∴ t = 4

- Substitute the values of P, r, n, and t in the formula above

∵
`A=800(1+(0.09)/(1))^((1)(4))`

∴
`A=800(1.09)^(4)`

∴ A = 1129.265

∴ The balance after four years is $1129.27