Assignment

1. Mary is considering a car loan that requires payments of $200 per month for the first year and payments of $400 per month during the second year. The annual interest rate is 12% (assume a 1% monthly interest rate) and payments being in one month. What is the present value of this two-year car loan?

Assuming that it is monthly compounded payment (1% monthly interest rate), the present value of the loan is $6,246.31

Calculation from BAII Plus:

Pmt: 400

I/Y: 12%/12=1%

N: 1 x 12 = 12

CPT PV = 4502.03

FV = 4502.03

Pmt: 200

I/Y: 12%/1 = 1%

N: 1 x 12 = 12

CPT PV = $6246.31

2. Mary has been approached by another salesperson to buy a new automobile with payments of $522.59 per month for 48 months on a $25,000 car after making a $4,000 down payment. What is the loan’s APR on Mary’s car purchase?

Pmt: 522.59

N: 4

principal: 21000

APR: 9%

Or, we can use excel and type in the following formula: =Rate(48,-522.59,21000) = 0.75% x 12 = 9%

3. At another car dealership a salesperson says to Mary’s son Peter, “Buy this new Car for $25,000 cash or, with appropriate down payment, pay $500 per month for 47 months at 8% interest.” Assuming that the salesperson does not offer a free lunch, calculate the “appropriate” down payment.

= 500 x ((1-(1/1.08^47))/0.8) = 6,081.88

Mary would have to put a down payment of 6081.88

4. Mary is looking at buying a new car for her son: How much must Mary deposit today in an account earning 6% annually to accumulate a 20% down payment to use in purchasing a car one year from now, assuming that the car’s current price is $20,000 and inflation will be 4%?

Mary will have to accumulate $3,924.53 in order to save enough for the 20% down payment.

$20,000 x 1.04 = 20,800

20,800 x 0.2 = 4160

FV: 4160

N: 1

I/Y: 6%

CPT PV =3,924.53

5. If four years of college is expected to cost Mary’s daughter, Ellen, $150,000, 18 years from now, how much must Mary deposit now (today) into an account that will average a...