Question

Scheduled payments of $1362, $718, and $1145 are due in one-and-a-half years, three-and-a-half years, and five-and-a-half years respectively. What is the equivalent single replacement payment two-and-a-half years from now if interest is 5.8% compounded quarterly? The equivalent single replacement payment is $ . (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

Computation of value of $ 1,362 on year two-and-half-year which is schedule on year one-and-half year:

FV = PV x (1+r) ⁿ

PV = $ 1,362

r = Periodic rate = 0.058/4 = 0.0145

n = 1-year x 4 periods = 4 periods

Value of $ 1,362 on two-and-half-year from now

= $ 1,362 x (1+0.0145) ⁴

= $ 1,362 x (1.0145) ⁴

= $ 1,362 x 1.059274

= $ 1,442.7308321163

Computation of Value of $ 718 on year two and -half-year which is schedule on three-and-half year:

PV = FV/(1+r) ⁿ

FV = $ 718

r = Periodic rate = 0.058/4 = 0.0145

n = 1-year x 4 periods = 4 periods

Value of $ 718 on two-and-half-year from now

= $ 718/ (1+0.0145) ⁴

= $ 718/ (1.0145) ⁴

= $ 718/ 1.059274

= $ 677.822735

Computation of Value of $ 1,145 on year two and -half-year which is schedule on three-and-half year:

PV = FV/(1+r) ⁿ

FV = $ 1,145

r = Periodic rate = 0.058/4 = 0.0145

n = 3-year x 4 periods = 12 periods

Value of $ 1,145 on year two and -half-year from now

= $ 1,145/ (1+0.0145) ¹²

= $ 1,145/ (1.0145) ¹²

= $ 1,145/ 1.18856959535234

= $ 963.342831986689

Total value of three cash flow on year two-and-half-year from now

= $ 1,442. 731188 + $ 677.822735 + $ 963.342504

= $ 3,083.896427 or $ 3,083.90

The equivalent replacement payment is $ 3,083.90