Question

please provide step by step explanation & reasoning it would be so incredible helpful

Question 28. A car costing $20,000 is purchased on finance by Monopoly Man from the Seller of SUV's. An initial down-payment of $4000 is made, and the balance is to be amortized by equal monthly installments over a period of four years. Given a repayment interest rate of 6% per annum compounded monthly: calculate how much of the first monthly payment is applied to the principal, and how much to interest. 3

Answer 1

Car Cost = $20,000

Down Payment = $4,000

Loan Amount = $16,000

Interest rate = 6% p.a

Interest rate (monthly) = 6/12 = 0.5% p.m

Loan period = 4 years

Loan period (months) 12*4 = 48 months

Firstly, we need to calculate the equal monthly repayment of Loan. To calculate this, use following equation -

$\textup{Equal monthly repayment} = \frac{\textup{Loan Amount}}{PVIFA(i,n)}$

where,

i = interest rate

n = no. of payment

putting the values -

$\textup{Equal monthly repayment} = \frac{\textup{16,000}}{PVIFA(0.005,48)}$

where,

${PVIFA(i,n)} = \frac{(1+i)^n-1}{i(1+i)^n}$

${PVIFA(0.0005,48)} = \frac{(1+0.005)^{48}-1}{0.005(1+0.005)^{48}}$

${PVIFA(0.0005,48)} = \frac{0.27048916109}{0.00635244580}$

${PVIFA(0.0005,48)} = 42.5803178186$

Thus,

$\textup{Equal monthly repayment} = \frac{\textup{16,000}}{42.5803178186}$

$\textup{Equal monthly repayment} = 375.76$

Equal monthly repayment = $375.76

Interest portion in first payment

Interest amount in first payment = 16,000*0.005 = $80

Principal portion in first payment

Principal in first payment = 375.76 - 80 = $295.76

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.