Question

In: Accounting

Joseph is considering a used car currently valued at $12,000. He can get an interest rate...

Joseph is considering a used car currently valued at $12,000. He can get an interest rate of 2.5% annually for a 5 year car loan. Joseph currently has $14,000 in a savings account and wants to use some of his savings for a down payment.
If Joseph decided to put $3,000 down as a down payment, what are his monthly payments?
If Joseph decided to put $5,000 down as a down payment, what are his monthly payments?
How much does Joseph save in interest if he puts $5,000 down compared to $3,000?
If Joseph decides to pay for the whole thing what could he potentially save in interest payments?
If Joseph can invest $12,000 in an 8% annual investment. Alternatively he is considering just paying cash for the car leaving him no payment. Which would you recommend and why? Include the numbers!!

Solutions

Expert Solution

Answer:

Value of Car      12,000.00
Rate of Interest 2.50%
Period (Years)                5.00
Down payment        3,000.00 Down payment                             5,000.00
Loan Value        9,000.00 Loan Value                             7,000.00
We Know, We Know,
Monthly Payment= PV*i Monthly Payment= PV*i
1-(1+i)^-n 1-(1+i)^-n
PV Loan Value     9,000.00 PV Loan Value    7,000.00
Instalments in a year          12.00 Instalments in a year         12.00
n 12*5          60.00 n 12*5         60.00
i 2.5%/12 0.21% 0.00208333333333333 i 2.5%/12 0.21% 0.00208333333333333
Monthly Payment= 9000*0.00208333333333333 Monthly Payment= 7000*0.00208333333333333
1-(1+0.00208333333333333)^-60 1-(1+0.00208333333333333)^-60
Monthly Payment= 18.75 Monthly Payment= 14.58333333
1-(1.00208333333333333)^-60 1-(1.00208333333333333)^-60
Monthly Payment= 18.75 Monthly Payment= 14.58333333
1-0.882611659150112 1-0.882611659150112
Monthly Payment= 18.75 Monthly Payment= 14.58333333
0.11738834 0.117388341
Monthly Payment ($)           159.73 Monthly Payment ($)                                124.23
Total payments        9,583.58 159.73*60 Total payments                             7,453.89 124.73*60
Loan Value        9,000.00 Loan Value                             7,000.00
Interest paid           583.58 Interest paid                                453.89
Difference in Interest paid        129.68
Joseph will save $ 129.68 in interest if he puts $5,000 down compared to $3,000.
If Joseph decides to pay for the whole thing he could have saved $ 453.89 in interest payments.
If Joseph can invest $12,000 in an 8% annual investment.
P      12,000.00
i 8% 0.08
Years                5.00
Interest amount P*((1+i)^n-1)
Interest amount 12000*((1+.08)^5-1)
Interest amount        5,631.94
Its better to take loan against car because Joseph can invest $ 12,000 which will earn him interest of $ 5,631.94.
It is much more than the total interest he has to pay on loan.

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