I am having trouble with a Finance problem, I can not figure out which time value formulas to use. The question is as follows:
You have $25,000 in an investment account earning 6% per year. You decide to purchase a new car with a sticker price of $25,000. The car dealer offers you either $3000 cash back or 0% financing for 5 years. If you take the financing, you will make 5 equal annual end of the year payments of $5,000. Otherwise, you will pay $22,000 today for the car. Based on the time value of money, which option should you take.
You have $25,000 in an investment account earning 6% per year. You decide to purchase a new car with a sticker price of $25,000. The car dealer offers you either $3000 cash back or 0% financing for 5 years. If you take the financing, you will make 5 equal annual end of the year payments of $5,000. Otherwise, you will pay $22,000 today for the car. Based on the time value of money, which option should you take.
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$22000 today is worth 22000*1.06^5 = $29440.96 after 5 yrs
5 equal end of the year payments after 5 years are worth
5000(1.06^5 - 1)/0.06 = $28,185.46 <--------
choose the latter option
5 equal end of the year payments after 5 years are worth
5000(1.06^5 - 1)/0.06 = $28,185.46 <--------
choose the latter option
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if you choose financing ur present value of all installment will be
NPV= 5000[{1-1/(1+i)^n}/i)
so 5000[{1-1/(1+.06)^5}/.06)
=$21061.81893
so if you pay 5000 yearly You will pay as NPV =$21061.81893
So as financing for the car dealer you could earn 938.1810722 more.
so you should choose financing.
NPV= 5000[{1-1/(1+i)^n}/i)
so 5000[{1-1/(1+.06)^5}/.06)
=$21061.81893
so if you pay 5000 yearly You will pay as NPV =$21061.81893
So as financing for the car dealer you could earn 938.1810722 more.
so you should choose financing.