Question

# National First Bank offers you a home loan for the next 30 years. The interest rate...

National First Bank offers you a home loan for the next 30 years. The interest rate on the loan is 2.5% per annum. Required: a. If the bank says that you need to pay \$500 each week and the interest rate is compounded weekly, what is the amount of your home loan? b. What is your monthly payment if you wish to pay monthly instalments and the interest rate is compounding monthly?

EMI = P*i*(1+i)^n/[{(1+i)^n}-1]

Where,

EMI = 500

i= Interest Rate = 0.025/52 = 0.00048

n= Number of periods = 30*52 = 1560

Therefore,

500 = P*0.00048*(1+0.00048)^1560/[{(1+0.00048)^1560}-1]

500 = P*0.00048*2.11408/1.11408

500 = P*0.0009108

Therefore, Loan Amount = P = 500/0.0009108 = \$548938.55

b)

EMI = P*i*(1+i)^n/[{(1+i)^n}-1]

Where,

P = Principal = 548938.55

i= Interest Rate = 0.025/12 = 0.002083

n= Number of periods = 30*12 = 360

Therefore, EMI = 548938.55*0.002083*(1+0.002083)^360/[{(1+0.002083)^360}-1]

= 1143.439*(2.115096)/[2.115096-1] = 2418.483/1.115096 = \$2168.86

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