Question

Suppose that $9500 is invested at 5.8%, compounded quarterly. Find the amount of money in the account after 8 years. Round your answer to the nearest dollar, and input it into the following box. Only NUMBERS are allowed in the input field.

Answer 1

The amount of money in the account after 8 years is $15,059

Explanation:

The formula for compound interest, including principal sum, is

`A=P(1+(r)/(n))^(nt)` , where

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

∵ $9500 is invested at 5.8%, compounded quarterly

∴ P = 9500

∴ r = 5.8% =
`(5.8)/(100)` = 0.058

∴ n = 4 ⇒ compounded quarterly

∵ The amount of money will be in the account for 8 years

∴ t = 8

Substitute all of these value in the formula above

∵
`A=9500(1+(0.058)/(4))^(4(8))`

∴
`A=9500(1.0145})^(32)`

∴ A = 15058.7613 dollars

- Round it to the nearest dollar

∴ A = 15059 dollars

The amount of money in the account after 8 years is $15,059