Ian has decided to buy a new car for $30,000 and agreed to make monthly payments for three years at 8.4% annual interest
a) How much is each payment?
b) How much total cumulative interest will he pay over the life of the loan?

Please help with step by step!!

Step-by-step explanation:

a) The cost of the house is $30000.

We would apply the periodic interest rate formula which is expressed as

P = a/{[(1+r)^n]-1}/[r(1+r)^n]

Where

P represents the monthly payments.

a represents the amount of the loan

r represents the annual rate.

n represents number of monthly payments.

From the information given,

a = $30000

r = 0.084/12 = 0.007

n = 12 × 3 = 36

Therefore,

P=30000/{[(1+0.007)^36]-1}/[0.007(1+0.007)^36]

P = 30000/{1.285 -1}/[0.007(1.285)]

P = 30000/[(0.285/0.008995

P = 30000/31.68

P = $947

b) The total amount that he would pay in 3years is

947 × 36 = 34092

The total cumulative interest is

34092 - 30000 = $4092