Answer:
Explanation:
To find out what Natalie would give as a monthly installment, we first need to calculate the monhly payment on a $35000 loan with 7.5% interest rate for 48 months using present value annuity formual.
PV = 35000
r= 7.5% = 7.5%/12 = 0.00625
t = 48
PMT = monthly payments
PMT = (r*PV) / [1 - (1+r)-n]
=( 0.00625* 35000) / [1-(1+0.00625)-48 ]
= 218.75 / [ 1 - (1.00625)-48 ]
= 218.75 / [ 1 - 0.74151 ]
= 218.75 / 0.25849
=$846.26
Monthly payment of $846.26
Total Cost = Monthly payment * 48
=$40620.56
For second loan option
r = 4.5%/12 = 0.00375
n = 36
PV = $35000
Using same formual
PMT = (r*PV) / [1 - (1+r)-n]
=( 0.00375* 35000) / [1-(1+0.00375)-36 ]
= 131.25 / [1 - (1.00375)-36 ]
= 131.25 / [ 1 - 0.873937 ]
= 131.25 / [ 0.126063
= $1041.42
Monthly payment of $1041.42
Total payment = 1041.42*36
= $37481.12
Thus, the 48 month or 4 year loan has monthly payment of $846.26 and total cost of $40620.56
And , the 36 month or 3 year loan has monthly payment of $1041.42 and total cost of $37481.12
