Question

1. After carefully going over your budget, you have determined you can afford to pay $632 per month toward a new sports car. You call up your local bank and find out that the going rate is 1 percent per month for 50 months. How much can you borrow?

2. Suppose you wish to start up a business that specializes in the latest health food trend, frozen milk. To produce and market your product, the Yakee Doodle Dandy, you need to borrow $100,000. Because it strikes you as unlikely that this particular fad will be long-lived, you propose to pay off the loan quickly by making five equal annual payments. If the interest rate is 18 percent, what will the payments be?

3. You have $6,000 to deposit. Bank A offers 12 percent per year compounded monthly (1 percent per month), while Bank B offers 12 percent but will only compound annually. How much will your investment be worth in 20 years at each bank?

4. You have decided that you want to have 1 million when you retire in 45 years. If you can earn an annual return of 11 percent, how much do you have to invest today?

Answer 1

We know that, EMI=[P*R*(1+R)^n]/[(1+R)^n-1]

where, EMI=Equated monthly installment, P=Pricipal loan amount, R=Rate of Interest & n=number of monthly installments.

Here we know that, EMI= $632, P=Pricipal or x (assume), R= 1% per month or 1/100 or 0.01 and n= 50 months

Now putting the values in the equation we get, $632 = [x*.01*(1+.01)^50]/[(1+.01)^50-1]

If we solve the problem, we will get x=Pricipal= $24771.95.

Therefore, If I can afford to pay an EMI of $632 per month then I can borrow an amount of $24771.95 for a tenure of 50 months.