Answer:
Monthly payment (A)
Interest rate (r) = 4% = 0.04
Number of years = 5 years
Number of times payment is made in a year (m) = 12
PV = A(1 - (1 + r/m)-nm)
r/m
PV = $600(1 - (1 + 0.04/12)-5)
0.04/12
PV = $600(1 - (1 + 0.0033)-5)
0.0033
PV = $600(1 - (1.0033)-5)
0.0033
PV = $600 x 4.950878649
PV = $2,971
Explanation:
In this case, we need to apply the formula for present value of ordinary annuity. The monthly payments, interest rate and number of years were provided in the question with the exception of present value. Therefore, we will make the present value the subject of the formula.
The loan amount that Rasheed could borrow for a new car is $12889.31 (approximately) which is calculated as the present value of the monthly payment.
Present value represents that amount of future cash flows in the terms of today. In simple words, present value is the current value of the future sum at a specified rate of interest.
The formula to calculate the present value of monthly payment is:
[tex]\rm Present \:value = Monthly\:payment \: \: \dfrac{(1 - (\dfrac{1}{(1 +r)^n}))}{r}\\\\\rm Present \:value = \$600\times \: \: \dfrac{(1 - (\dfrac{1}{(1 + 0.04)^{60}}))}{0.04}\\\\\rm Present \:value = \$600\times \: \: \dfrac{(1 - (\dfrac{1}{(1.04)^{60}}))}{0.04}\\\\\rm Present \:value = \$600\times \: \: \dfrac{(1 - 0.0813)}{0.04}\\\\\rm Present \:value = \$600\times \: \: \dfrac{0.9187}{0.04}\\\\\\\rm Present \:value = \$600\times \: 22.9685\\\\[/tex]
Therefore, the present value is $12889.31. Hence the loan amount can be $12889.
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