Question

116. Used Motors will sell you a $16,000 car with financing for 48 months at an APR of 12%. Assuming interest compounds monthly, what is your required monthly payment? Show calculations or calculator inputs.

Answer 1

Monthly payment of $421.34 is required

As requured to calculate Monthly payment , Annuity formula will apply.

Formula for Annuity

P =A (1-1/(1+r)ⁿ)/r

Where P = Present value Principal Amount

A= annual payment to be made

r=Rate of Interest =12/12 as compounded monthly =1%

n = Number of times or period in which payment is to be made =48 month

From Above formula we get

A =( P ×r ) (1+r)ⁿ /(1+r)ⁿ-1

A = 16000 × 0.01 (1.01)⁴⁸/ [(1.01)⁴⁸-1

=160×1.61223/(1.61223-1)

=257.9568/0.61223

=421.3396

Please find the attached file if solve through Excel

B 106 107 108 109 110 111 112 113 114 115 Principle Annual Payment Rate Number of Month 16000 =12%/12 48 =+PMT(C115,C116,-C114) 116 117 118 119 120 121 122 123 124 A B С 106 107 108 109 110 111 112 113 114 16000 115 Principle Annual Payment Rate Number of Month 1% 116 48 117 $421.34 118 119 120