Question

a) Kathy promised to pay her sister Suzie $4000 in six years in return for dental services to be performed immediately. Suzie prefers Kathy pay in installments, so Kathy agrees to make equal, monthly payments over the next six years. If Kathy’s opportunity cost is three percent, how much must Kathy pay each month?

b) If Kathy makes her payments at the beginning of each month, how much must Kathy pay?

a. $50.77 b. $50.65

I just need help for b

Answer 1

Requirement - (b)

Future Value of an Annuity Due is calculated by using the following Formula

Future Value of an Annuity Due = (1 + r) x P x [{(1+ r) ⁿ - 1} / r]

Future Value = $4,000

Monthly Interest rate (r) = 0.25% per month [12% / 12 Months]

Number of months (n) = 72 Months (6 Years x 12 Months)

Monthly Payment (P) = ?

Future Value of an Annuity Due = (1 + r) x P x [{(1+ r) ⁿ - 1} / r]

$4,000 = (1 + 0.0025) x P x [{(1 + 0.0025)⁷² – 1} / 0.0025]

$4,000 = 1.0025 x P x [(1.196948 – 1) / 0.0025]

$4,000 = 1.0025 x P x (0.196948 / 0.0025]

$4,000 = 1.0025 x P x 78.77938

$4,000 = P x 78.97633

P = $4,000 / 78.97633

P = $50.65

“Therefore, the Kathy must pay $50.65 at the beginning of each month”