# 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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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

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