Racecar Rita can afford a $450 per month car payment. She found a 5-year loan at a 3% interest rate. How big of a loan can Racecar Rita afford? Round to the nearest cent.
Solution
Here the Present value of the loan payments will be equal to the largest loan that can be taken
The formula for Present value of ordinary annuity is given below
Present value of annuity=Loan amount=Annuity payment*((1-(1/(1+i)^m))/i)
where
i-discount or intrest rate per period-3/12=.25% per month
m-number of periods =5*12=60
Present value of annuity =Loan amoun she can rais=?
Annuity payment=Monthly payment=450
Putting values in formula
Present value of annuity=450*((1-(1/(1+.0025)^60))/.0025)
Solving we get
Present value of annuity =25043.56
Thus the loan Racecar Rita can afford is $25043.56
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