Question

When you purchased your? car, you took out a? five-year annual-payment loan with an interest rate of 5.7% per year. The annual payment on the car is $4,900.

You have just made a payment and have now decided to pay off the loan by repaying the outstanding balance. What is the payoff amount for the following? scenarios?

**a.**You have owned the car for one year? (so
there are four years left on the? loan)?

**b.** You have owned the car for four years? (so
there is one year left on the? loan)?

2. Your grandmother has been putting $5,000 into a savings account on every birthday since your first? (that is, when you turned? one). The account pays an interest rate of 9%.

How much money will be in the account immediately after your grandmother makes the deposit on your 18th birthday

Answer #1

1) Using excel sheet below

a) Pay off after one year = 17096.31

b)Pay off after four years = 4635.76

Formulas | PMT FUNCTION= PMT(0.55%,360,570,000) | InterestPaid = Interest rate per period * beginning balance | Beginning balance - Interest Period | Ending Balance = Beginning Balance - Principal Paid | |

Payment No | Beginning balance | Payment Amount | Interest Paid | Principal Paid | Ending Balance |

1 | 20,810.13 | $4,900.00 | 1186.18 | $3,713.82 | $17,096.31 |

2 | 17,096.31 | $4,900.00 | 974.49 | $3,925.51 | $13,170.80 |

3 | 13,170.80 | $4,900.00 | 750.74 | $4,149.26 | $9,021.53 |

4 | 9,021.53 | $4,900.00 | 514.23 | $4,385.77 | $4,635.76 |

5 | 4,635.76 | $4,900.00 | 264.24 | $4,635.76 | ($0.00) |

2)Amount of money deposited by grandmother till 18th birthday =
money deposited on birthday + FV of 17 annuities of $5000 = 5000 +
5000 *[(1+r)^{n}-1]/r = 5000 + 5000*[(1+9%)-1]/9% =5000+
184868.82 = 189868.20

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