Business, 16.11.2020 16:40 naomicervero

Don takes out a personal loan for $12000 to fund his wedding. He will repay it over 5 years at 6% p. a. Calculate the:

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Answer from: gianni0

(a)Total repayment = $16,185.95

(b) Monthly repayment = $231.99.

Explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Don takes out a personal loan for $12000 to fund his wedding. He will repay it over 5 years at 6% p.a. Calculate the:

(a) Monthly repayment

(b) Total repayment

The explanation to the answers is now provided as follows:

(a) Monthly repayment

This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value of the of the loan or the loan amount = $12,000

P = Monthly repayment = ?

r = Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005

n = number months = 5 years * 12 months = 60

Substitute the values into equation (1) and solve for P, we have:

$12,000 = P * ((1 - (1 / (1 + 0.005))^60) / 0.005)

$12,000 = P * 51.7255607511308

P = $12,000 / 51.7255607511308

P = $231.99

Therefore, monthly repayment is $231.99.

(b) Total repayment

This can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:

FV = M * (((1 + r)^n - 1) / r) (2)

Where;

FV = Future value of the loan or total repayment = ?

M = Monthly repayment = $231.99

r = Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005

n = number months = 5 years * 12 months = 60

Substitute the values into equation (2), we have:

FV = $231.99 * (((1 + 0.005)^60 - 1) / 0.005)

FV = $231.99 * 69.7700305098607

FV = $16,185.95

Therefore, total repayment is $16,185.95.

This can be calculated as follows:

Interest charged = Total repayment - Loan amount = $16,185.95 - $12,000 = $4,185.95.

Therefore, interest charged is $4,185.95.

Answer from: Quest

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Answer from: Quest

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