1. You want to buy a $50,000 car to make others more jealous of your awesome rid
ID: 1137345 • Letter: 1
Question
1. You want to buy a $50,000 car to make others more jealous of your awesome ride. You need to loan the entire cost of the car with 0.25% interest rate per month. You don’t remember the payback period of the loan but you have to pay $1,000 a month for the car. Find the payback period for your awesome car. [This problem is partially designed based on your submitted stories.]
2. Your dad promised your mom that he will put aside $1,000 each year for you and your sibling since when you were born and give back the invested money to you at your 18th birthday. He invested your money in a share market with an average annual interest rate of 10%. The only difference is that you will receive this money as a result of 10% simple interest and your sibling will receive the money as a result of investment in 10% compound interest. How much more money your sibling received out of these investments?
Explanation / Answer
ANSWER:
1) Present value of car = $50,000
i = 0.25% per month
monthly amount to be paid = $1,000
n =?
present value = amount(p/a,i,n)
50,000 = 1,000(p/a,0.25%,n)
50,000 / 1,000 = (p/a,0.25%,n)
50 = (p/a,0.25%,n)
finding the value of n in the compounding tables we get n = 53 and 54 years that is 53.5 years approx.
2) amount put aside by dad = $1,000
i = 10% and n = 18 years
money recieved by my sibling = amount put aside by dad(f/a,i,n)
money recieved by my sibling = 1,000(f/a,10%,18)
money recieved by my sibling = 1,000 * 45.599 = $45,599
money recieved by me in 1 year = amount put aside by dad + i * amount put aside by dad
money recieved by me in 1 year = 1,000 + 10% * 1,000
money recieved by me in 1 year = 1,000 + 100 = 1,100
money recieved by me in 18 years = money recieved by me in 1 year * 18 = 1,100 * 18 = $19,800
more money recieved by my sibling = money recieved by my sibling - money recieved by me in 18 years = $45,599 - $19,800 = $25,799.17
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