Question

Find the interest on an investment of $45,000

compound annually at 5.25% for 6 years
A = P(1 + r)t

Answer 1

The interest on the investment is $16,170.93811

Explanation:

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

• A is the new value

• P is the initial value

• r is the rate in decimal

• n is the number of periods in time

• t is the time

∵ The investment is $45,000

∴ P = 45,000

∵ The interest on the investment is compounded annually at 5.25%

∴ r = 5.25% = 5.25 ÷ 100

∴ r = 0.0525

∴ n = 1 ⇒ compound annually

∵ It is for 6 years

∴ t = 6

→ Substitute them in the rule above

∵
`A=45,000(1+(0.0525)/(1))^(1(6))`

∴
`A=45,000(1.0525)^(6)`

∴ A = 61,170.93811

∵ I = A - P, where I is the interest

∴ I = 61,170.93811 - 45,000

∴ I = 16,170.93811

∴ The interest on the investment is $16,170.93811