PV and loan eligibility You have saved $5,000 for a down payment on a new car. T
ID: 2383827 • Letter: P
Question
PV and loan eligibility
You have saved $5,000 for a down payment on a new car. The largest monthly payment you can afford is $450. The loan will have a 9% APR based on end-of-month payments.
a) What is the most expensive car you could afford if you finance it for 48 months? Round your answer to the nearest cent.
a) What is the most expensive car you could afford if you finance it for 60 months? Round your answer to the nearest cent.
Reaching a financial goal
Erika and Kitty, who are twins, just received $35,000 each for their 26th birthdays. They both have aspirations to become millionaires. Each plans to make a $5,000 annual contribution to her "early retirement fund" on her birthday, beginning a year from today. Erika opened an account with the Safety First Bond Fund, a mutual fund that invests in high-quality bonds whose investors have earned 5% per year in the past. Kitty invested in the New Issue Bio-Tech Fund, which invests in small, newly issued bio-tech stocks and whose investors have earned an average of 14% per year in the fund's relatively short history.
a) If Erika's fund earns the same returns in the future as in the past, how old will she be when she becomes a millionaire? Round your answer to two decimal places.
years
b) If Kitty's fund earns the same returns in the future as in the past, how old will she be when she becomes a millionaire? Round your answer to two decimal places.
years
c) How large would Erika's annual contributions have to be for her to become a millionaire at the same age as Kitty, assuming their expected returns are realized? Round your answer to the nearest cent.
d) Is it rational or irrational for Erika to invest in the bond fund rather than in stocks?
Explanation / Answer
Solution:
The price of most expensive car will be eaqual to the total money avaiable after 48 months
Given, rate of APR = 9 % which is yearly, monthly = 9% / 12 months = 0.75 % per period or month
Number of periods, n = 48 months
Now, total money available = $ 5,000 ( down payment ) + Future value = annuity value × [(1 + r)n - 1] / r
= $ 5,000 + Annuity Value = $ 480 * [(1 + 0.75 %) * 48 - 1] / 0.75
= $ 5,000 + $ 27,610
The most expensive car that is affordable is = $ 32,610
If, n changed to 60 months, then
Now, total money available = $ 5,000 ( down payment ) + Future value = annuity value × [(1 + r)n - 1] / r
= $ 5,000 + Annuity Value = $ 480 * [(1 + 0.75 %) * 60 - 1] / 0.75
= $ 5,000 + $ 36,204
The most expensive car that is affordable is = $ 41,204.
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