# The Nguyen family buys a car for $32000, paying a deposit of $5000 and taking out a loan for the balance. If the loan is over 5 years and interest is charged at 1.5% monthly, find the amount of the...

The Nguyen family buys a car for $32000, paying a deposit of $5000 and taking out a loan for the balance. If the loan is over 5 years and interest is charged at 1.5% monthly, find the amount of the monthly loan repayments. How much will the family pay for the car together?

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### 1 Answer

The car costs $32000 less the deposit $5000. The loan is $27000.

Use the formula: `P=(x[1-(1+i)^-n])/i`

P=27000, n=5 years x 12 months= 60, i=1.5% pm = 0.015.

Note, as interest is charged monthly, this infers compound interest

`therefore 27000= (x[1-(1+0.015)^-60])/0.015` Care not to round off too soon

`therefore (27000 times 0.015)/([1-(1.015)^-60])=x `

`therefore x=$685.62`

Remember to add the $5000 back to the instalments when calculating the total cost of the vehicle:

`$685.62 times 60 = 41137.20 + $5000`

`= $46137.20`

**Ans: The repayments are $685.62 per month and the total repayment therefore is $46 137.20**