# Calculating EMI for a loan

You want to buy a car. Based on your current finances, you have up to $3,200 in savings that you can use for a down payment. You believe you can afford no more than $160 per month in loan payments.

Offer Number 1: An individual you trust will sell you a used car for 10% off the Blue Book value of $9,800. Your company credit union offers used car loans for 48 months at 7Â½ % annual simple interest.

For Offer Number 1

1.How much will the car cost after the discount?

2.How much will you need to borrow from your credit union?

3.What is the total amount of interest paid in 48 months?

4.How much will the monthly payments be?

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Solution:

For Offer Number 1

1. How much will the car cost after the discount?

Cost of the car after discount=9800*(1-10%)=$8820

2. How much will you need to borrow from your credit union?

Loan amount =8820-3200=$5620

3. What is the total amount of interest paid in 48 months?

Monthly installment=$135.89 (refer part 4)

Amount Paid in 48 months=$135.89*48=$6522.72

Total interest paid=6522.72-5620=$902.72

4. How much will the monthly payments be?

We know PV of any ordinary annuity is given by

Where i=interest rate per period=7.5%/12=0.6250%

N=number of periods =48

R=periodic payment

5620=R*41.35837

R=5620/41.35837=135.89

Monthly payment will be $135.89

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