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Emily wants to buy a new car for $25,300, including all fees and taxes. “Now’s a good time to buy,” claims the salesman, “we’re offering 4 year loans at 5.9%. Even if you have the cash, you’re bett

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1. Emily wants to buy a new car for $25,300, including all fees and taxes. “Now’s a good
time to buy,” claims the salesman, “we’re offering 4 year loans at 5.9%. Even if you
have the cash, you’re better off borrowing.” Emily is confused.
The salesman goes on to explain the payment on the car loan would be $593.01, which
means that total interest paid on the loan will be $3,164.48. By investing the $25,300
at current savings account rates of 3.5% (compounded monthly), Emily could generate
interest of $3,796.0...

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Question Preview:

1. Emily wants to buy a new car for $25,300, including all fees and taxes. “Now’s a good
time to buy,” claims the salesman, “we’re offering 4 year loans at 5.9%. Even if you
have the cash, you’re better off borrowing.” Emily is confused.
The salesman goes on to explain the payment on the car loan would be $593.01, which
means that total interest paid on the loan will be $3,164.48. By investing the $25,300
at current savings account rates of 3.5% (compounded monthly), Emily could generate
interest of $3,796.00 which means she’d be $631.52 better off by investing her money
in a savings account.
(a) Verify the numbers in the second paragraph.
(b) Is Emily really better off by borrowing the money for her new car?
2. John and Jane Smith have just received a quote for home, car and liability insurance.
The annual premium amounts to $3,500. They are given the choice of paying i) the
entire amount in advance, ii) $310 per month with the first and last month due in
advance; or iii) $920 per quarter, payable on the first of every quarter.
(a) Calculate the rates being charged for Options (ii) and (iii).
(b) Suppose the Smiths have exactly $3,500 in the bank, and suppose they can either
borrow or lend at 15% compounded monthly. What do you recommend?
3. A recent newspaper advertisement offered car buyers the opportunity to lease a new
vehicle for $5,000 down plus $350 per month for 48 months. At the end of the 48
months, the car will be returned to the dealer. Alternatively, the same car could be
purchased outright for $34,000. It is estimated that in 48 months, the car could be
sold for $20,000.
At what interest rate (compounded monthly) are these two options equivalent?
 

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Solution preview

Question 1

a)

For Loan

Price of car = 25300

Interest rate = 5.9%

Time = 4

We know,

A = P*(1+r)^n

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