The purchase of the car that Joe dreams about can be accomplished by making paym
ID: 2420138 • Letter: T
Question
The purchase of the car that Joe dreams about can be accomplished by making payments of $300 a month for six years, if the first payment is made on February 1, 1995, and the last payment is made on January 1, 2001. The financing company charges 6% nominal interest rate compounded monthly. Joe wants to be able purchase the ear for cash on January 1, 1995, just after he graduates from college. Joe has a job and started making depositing of $275 each month into an account that pays 9% compounded monthly beginning with the first deposit on February 1, 1990. The last deposit is to be made on January 1, 1995. Will Joe have saved up enough money to purchase the car? If not, how much should Joe be saving each month if all Oliver conditions remain the same?Explanation / Answer
To Arrive at the answer here we need to calculate two things
1) The Cost of the new car
2) The total amount saved by Joe at the end of the tenure of the deposit
If the deposits saved by Joe is more then the cost of the car then buying car will bw possible
1) Cost of the Car is not given however the the monthly payments to be made is given with the interest rate and period for which the payments need to be made - Thus using the below formula formula of EMI we can arrive at the principal and that is the cost of the Car as no mention of Down payment we assume that the car was fully ie 100 % financed and the montly EMI paid covers the cost of the car
Where
here use the monthly rate and tenure as interest is calculated monthly
Substituting the values in formula we have P = 18102 = Cost of the car
2) Now using the formula for recurring deposit for 5 years with inetrest rate of 9% we can find the total saving
M = ( R x [ (1+r)power n - 1] ) / [1- ( 1+ r) power (-1)]
Where
After Solving the above formula we have total saving of $20897
Thus joe can save enough to buy the car
EMI = ( P × r × (1+r)n ) / ((1+r)n 1)Related Questions
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