Question

Cooley's landscaping needs to borrow $28,000 for a new front-end dirt loader. the bank is willing to loan the money at 8.5% interest for the next 5 years with annual, semiannually, quarterly, or monthly payments. what are the different payments that Cooley landscaping could choose for these different payment plans?

Answer 1

(a)-Annual Payment

Loan Amount (P) = $28,000

Interest Rate (n) = 8.50%

Number of years (n) = 5 Years

Annual Payment = [P x {r (1+r)ⁿ} ] / [( 1+r)ⁿ – 1]

= [$28,000 x {0.085 x (1 + 0.085)⁵}] / [(1 + 0.085)⁵ – 1]

= [$28,000 x {0.085 x 1.50365}] / [1.50365 – 1]

= [$28,000 x 0.127810] / 0.50365

= $7,105.44 per year

(b)-Semi-annual Payment

Loan Amount (P) = $28,000

Interest Rate (n) = 4.25% [8.25% x ½]

Number of years (n) = 10 Years [5 Years x 2]

Annual Payment = [P x {r (1+r)ⁿ} ] / [( 1+r)ⁿ – 1]

= [$28,000 x {0.0425 x (1 + 0.0425)¹⁰}] / [(1 + 0.0425)¹⁰ – 1]

= [$28,000 x {0.0425 x 1.51621}] / [1.51621 – 1]

= [$28,000 x 0.06443] / 0.51621

= $3,495.24 per 6 month

(c)-Quarterly Payment

Loan Amount (P) = $28,000

Interest Rate (n) = 2.125% [8.50% x ¼]

Number of years (n) = 20 Years [5 Years x 4]

Annual Payment = [P x {r (1+r)ⁿ} ] / [( 1+r)ⁿ – 1]

= [$28,000 x {0.02125 x (1 + 0.02125)²⁰}] / [(1 + 0.02125)²⁰ – 1]

= [$28,000 x {0.02125 x 1.52279}] / [1.52279 – 1]

= [$28,000 x 0.032359] / 0.52279

= $1,733.11 per Quarter

(d)-Monthly Payment

Loan Amount (P) = $28,000

Interest Rate (n) = 0.708333% [8.50% x 1/12]

Number of years (n) = 60 Years [5 Years x 12]

Annual Payment = [P x {r (1+r)ⁿ} ] / [( 1+r)ⁿ – 1]

= [$28,000 x {0.00708333 x (1 + 0.00708333)⁶⁰}] / [(1 + 0.00708333)⁶⁰ – 1]

= [$28,000 x {0.00708333 x 1.52730}] / [1.52730 – 1]

= [$28,000 x 0.01081] / 0.52730

= $574.46 per month