Question

Suppose your friends parents invest $20,000 in an account paying 5% compounded annually. What will the balance be after 5 years?

Answer 1

The balance will be $25,525.63125 after 5 years

Explanation:

The formula of the compounded interest is A = P
`(1+(r)/(n))^(nt)` , where

• A is the new value

• P is the initial amount of investment

• r is the rate in decimal

• n is the number of periods per year

• t is the time in years

∵ Your friends' parents invest $20,000 in an account

∴ P = 20,000

∵ The account pays 5% compounded annually

∵ r = 5% ⇒ divide it by 100 to change it to decimal

∵ 5% = 5 ÷ 100 = 0.05

∴ r = 0.05

∵ n = 1 ⇒ compounded annually

∵ The time is 5 years

∴ t = 5

→ Substitute these values in the formula above

∵ A = 20,000
`(1+(0.05)/(1))^(1(5))`

∴ A = 20,000
`(1.05)^(5)`

∴ A = 25,525.63125

∴ The balance will be $25,525.63125 after 5 years