Question

You would like to save annually for buying a car 6 years from today. Suppose the first deposit is made today and the last deposit will be made 5 years from now. Assume the car will cost you $30,000 and your deposits earn you interest at 6% p.a, compounded annually.

(a) What is your annual deposit amount?

(b) Instead of making annual deposits, you would like to make your deposit monthly and the bank is happy to pay your interest on a monthly basis. What is the APR that would make the bank indifferent to these two way of paying interest?

(c) Assuming you make the deposit of $300 at the end of each month and the first deposit will be made one month from today, use the answer to part (b) calculate how much your deposits would accumulate to 6 years later.

(d) Assume 6 years later, the car price has gone up to $35,000. You decide to use the accumulated deposit as the down payment and take up a 2-year car loan. What would your monthly payment be if the interest rate is 7.5% and compounded monthly?

Answer #1

a] | Annual deposit = 30000*(0.06)/((1.06)*(1.06^6-1) = |
$
4,057.43 |

b] | 6% should be the effective interest rate | |

So, 0.06 = (1+r)^12-1, where t = APR/12 | ||

r = (0.06+1)^(1/12)-1 = | 0.486755% | |

APR = r*12 = | 5.84% | |

c] | FV = 300*((1+0.0584/12)^72-1)/(0.0584/12) = |
$
25,793.59 |

d] | Loan amount = 35000-25793.59 = | $ 9,206.41 |

Monthly payment = 9206.41*(0.0584/12)*(1+0.0584/12)^24/((1+0.0584/12)^24-1) = |
$
407.37 |

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