Respuesta :
Answer:
(a)Total repayment = $16,185.95
(b) Monthly repayment = $231.99.
(c) Interest charged = $4,185.95
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
(c) Interest charged.
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.
(c) Interest charged
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.
