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Jack took out a 6-year loan for $25,000 to purchase a boat at a 4.5% interest rate. If the interest is compounded monthly, what will he have paid total over the course of the loan?

Respuesta :

Parrain

Answer: $32,732.58

Step-by-step explanation:

To calculate the total loan payment over the course of the loan period, use the future value formula:

= Loan amount * (1 + rate) ^ number of years

As this loan is compounded monthly, you need to convert certain terms to monthly figures:

Number of periods = 6 * 12 months = 72 months

Interest = 4.5 / 12 = 0.375%

Total payment:

= 25,000 * ( 1 + 0.375%)⁷²

= $32,732.58

abidemiokin

He will have to pay $34,236.31 over the course of the loan.

Using the compound interest formula expressed as:

[tex]A =P(1+r/n)^{nt}[/tex]

P is the principal = $25000

r is the rate = 4.5% = 0.045

t is the time in years = 6 years

n is the compounding amount = (12)monthly

Substitute into the formula:

[tex]A =25000(1+0.045/12)^{12(7)}\\A=25000(1.36945)\\A = \$34,236.31[/tex]

Hence he will have to pay $34,236.31 over the course of the loan

Learn more on compound interest here: https://brainly.com/question/24274034

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