5, (20 points) You sell a $300 a month, 48 month annuity to XYZ Bank at 9% inter

Question

5, (20 points) You sell a $300 a month, 48 month annuity to XYZ Bank at 9% interest. So you agree to pay $300 every month for 48 months. The account is compounded monthly. For how much did you sell the annuity? (Hint: Use R from the previous problem) o 3 6. (5 points) Using results from the previous question, if you were shopping for a car and could afford a 300-a-month payment on a loan from a bank that gives you 9% interest compounded monthly for 48 months, then what is the maximum priced car you car shop for?

Explanation / Answer

Future value of annuity = periodic payment*[(1+r/t)^(n*t)-1]/(i)

where periodic payment = 300

r - rate of interest(9%)

t - no. of compounding interest 12

n - no. of periods 48

= 300*[(1+0.09/12)^48-1]/(0.09/12)

= 300*[1.431405-1]/0.0075

= 300*0.431405/0.0075

= 129.4216/0.0075

= 17256.21

6. here we should calcute the present value of annuity which would be

= Periodic payment*[1-(1+i/t)^(-n*t)]/(i)

= 300*[1-(1+0.09/12)^(-48)]/(0.09/12)

= 300*[1-0.698614]/0.0075

= 300*0.301386/0.0075

= 90.41576/0.0075

= 12055.43

Please comment in case of further clarification.

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