An installment contract for the purchase of a car requires payments of $337

Part A:

Amount financed is PV of Instalments( Annuity ).

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period.
PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 337.02 * [ 1 - [(1+0.005)^-63]] /0.005
= $ 337.02 * [ 1 - [(1.005)^-63]] /0.005
= $ 337.02 * [ 1 - [0.7304]] /0.005
= $ 337.02 * [0.2696]] /0.005
= $ 18174.69

Amount financed is $ 18174.69.

Part B:

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period.
FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 337.02 * [ [ ( 1 + 0.005 ) ^ 63 ] - 1 ] / 0.005
= $ 337.02 * [ [ ( 1.005 ) ^ 63 ] - 1 ] / 0.005
= $ 337.02 * [ [1.3692] - 1 ] / 0.005
= $ 337.02 * [0.3692] /0.005
= $ 24884.49

Int:

= FV of annuity - [ Instalment * No. of instalments ]

= $ 24884.49 - [ $ 337.02 * 63 ]

= $ 24884.49 - $ 21232.26

= $ 3652.23