Question

Payments of $1200 at the end of each month for the next 5 year(s) are equivalent to a single payment of $X now (t=0). If interest is 14.1% p.a. compounding monthly, then $X is (to the nearest cent, do not show dollar sign or commas eg $2,185.6323 is shown 2185.63) :

Answer 1

Calculation of single payment as of now (also referred to as Present value of ordinary monthly payments) :-

interest rate (i) = 14.1 % / 12 = 1.175 % or 0.01175 per month compounded. (Number of months in year = 12)

Time period = 5 * 12 = 60 months.    (Number of months in year = 12) (Compounding is monthly)

Present value = Payment per month * [ 1 - (1 + interest rate)- Time period / interest rate ]

= 1200 * [ 1 - (1 + 0.01175)-60 / 0.01175 ]

= 1200 * [ 1 - (1.01175)-60 / 0.01175 ]

= 1200 * [ 1 - 0.4961 / 0.01175 ]

= 1200 * 0.5039 / 0.01175

= 1200 * 42.8851

= 51462.12

Concluson :- Single payment as of now (Present value) = 51462.12 (approx).