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

Answer:

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

Step-by-step explanation:

The formula for compound interest, including principal sum, is

$A=P(1+\frac{r}{n})^{nt}$ , 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% = $\frac{5.8}{100}$ = 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

∵ $A=9500(1+\frac{0.058}{4})^{4(8)}$

∴ $A=9500(1.0145})^{32}$

∴ 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