Question

1. You want to start saving for your daughter's college education now. She will enter college at age 18 and will pay fees of $5,000 at the end of each of the four years. You will start your savings by making a deposit in one year and at the end of every year until she begins college. If annual deposits of $3,960.46 will allow you to reach your goal, how old is your daughter now? Assume you can earn 6% annual interest on your savings. (Hint: this needs to be calculated in 2 parts).

2. You plan to buy an Audi A8 on your 26th birthday. You have priced these cars and found that they currently sell for $85,100. You believe that the price will increase by 8% per year until you are ready to buy. You can presently invest to earn 10% annually. If you have just turned 20 years old, how much must you invest per year to be able to purchase the Audi according to your plans?

3.You have won a game show prize of a trip across Europe in one year valued at $30,000. If instead, you are able to take the present value of the trip in cash, how much cash would you want if the rate you can earn is 6% annually, compounded quarterly?

Answer 1

1]

First, we calculate the amount required at the beginning of the first year of college, in order to fund the 4 years of college fees.

Amount required is calculated using PV function in Excel :

rate = 6%

nper = 4

pmt = -5000

PV is calculated to be $17,325.53

Next, we calculate the number of years required to reach the target amount of $17,325.53

Number of years is calculated using NPER function in Excel :

rate = 6%

pmt = -3960.46

pv = 0

fv = 17325.53

NPER is calculated to be 4 years

number of years required to reach the target amount is 4 years.

Therefore, daughter's age now = 18 - 4 = 14 years