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1) Carmen Hernández has saved $ 8,000 for a car deposit

Finance Feb 27, 2021

1) Carmen Hernández has saved $ 8,000 for a car deposit. The highest monthly payment she can afford is $ 455. The loan will have an APR of 11% due at the end of each month. Determine what is the most expensive car you can buy if you buy it on credit payable in 60 months. 

2) Determine the present value of a financial instrument that pays $ 18,500 in 10 years if similar risk instruments pay 6% per year. 

3) Calculate the future value (FV) of a $ 5,000 investment at an interest rate of 10% over 7 years.

4) Determine the interest rate you will pay, if you are approved for a loan for $ 112,000 with annual payments of $ 15,000 over 8 years.

Expert Solution

1) We can calculate the present value by using the following formula in excel:-

=-pv(rate,nper,pmt,fv)

Here,

PV = Present value

Rate = 11%/12 = 0.9167% (monthly)

Nper = 60 periods (monthly)

Pmt = $455

FV = $0

Substituting the values in formula:

= -pv(0.9167%,60,455,0)

= $20,926.83

Maximum price = Present value + Down payment

= $20,926.83 + $8,000

= $28,926.83

 

2) Computation of the present value:-

FV = PV*(1+rate)^n

$18,500 = PV*(1+6%)^10

PV = $18,500 / 1.7908

= $10,330.30

 

3) Computation of the present value:-

FV = PV*(1+rate)^n

= $5,000*(1+10%)^7

= $5,000*1.9487

= $9,743.59

 

4) We can calculate the interest rate by using the following formula in excel:-

=rate(nper,pmt,-pv,fv)

Here,

Rate = Interest rate

Nper = 8 periods

Pmt = $15,000

PV = $112,000

FV = $0

Substituting the values in formula:

= rate(8,15000,-112000,0)

= 1.56%

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