A contract requires payments of $2,000 and $3,000, 90 days and 120 days, respectively, from today. What is the value of the contract today if the payments are discounted to yield a rate of return of 12% simple interest?

A) $4,824.06
B) $4,828.66
C) $4,831.48
D) $4,837.87
E) $5,177.53

Question

Molly Brown · Accepted Answer

Final Answer : B, Explanation :   To find the present value of the contract today, we discount each payment separately using the formula for simple interest:   P V = F V 1 + r t PV = \frac{FV}{1 + rt} P V = 1 + r t F V ​  , where   P V PV P V   is the present value,   F V FV F V   is the future value,   r r r   is the annual interest rate, and   t t t   is the time in years.For the $2,000 payment in 90 days (0.25 years):  P V 1 = 2000 1 + 0.12 × 0.25 = 2000 1 + 0.03 = 2000 1.03 = $ 1 , 941.75 PV_1 = \frac{2000}{1 + 0.12 	imes 0.25} = \frac{2000}{1 + 0.03} = \frac{2000}{1.03} = \$1,941.75 P V 1 ​ = 1 + 0.12 × 0.25 2000 ​ = 1 + 0.03 2000 ​ = 1.03 2000 ​ = $1 , 941.75  For the $3,000 payment in 120 days (0.33 years):  P V 2 = 3000 1 + 0.12 × 0.33 = 3000 1 + 0.0396 = 3000 1.0396 = $ 2 , 886.91 PV_2 = \frac{3000}{1 + 0.12 	imes 0.33} = \frac{3000}{1 + 0.0396} = \frac{3000}{1.0396} = \$2,886.91 P V 2 ​ = 1 + 0.12 × 0.33 3000 ​ = 1 + 0.0396 3000 ​ = 1.0396 3000 ​ = $2 , 886.91  Adding the present values of both payments:  P V t o t a l = P V 1 + P V 2 = $ 1 , 941.75 + $ 2 , 886.91 = $ 4 , 828.66 PV_{total} = PV_1 + PV_2 = \$1,941.75 + \$2,886.91 = \$4,828.66 P V t o t a l ​ = P V 1 ​ + P V 2 ​ = $1 , 941.75 + $2 , 886.91 = $4 , 828.66

A contract requires payments of $2,000 and $3,000, 90 days and 120 days, respectively, from today. What is the value of the contract today if the payments are discounted to yield a rate of return of 12% simple interest?

A) $4,824.06
B) $4,828.66
C) $4,831.48
D) $4,837.87
E) $5,177.53

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Learning Objectives

Related questions

A contract requires payments of $2,000 and $3,000, 90 days and 120 days, respectively, from today. What is the value of the contract today if the payments are discounted to yield a rate of return of 12% simple interest?A) $4,824.06B) $4,828.66C) $4,831.48D) $4,837.87E) $5,177.53

Definitions

Learning Objectives

Learning Objectives

Related questions

A contract requires payments of $2,000 and $3,000, 90 days and 120 days, respectively, from today. What is the value of the contract today if the payments are discounted to yield a rate of return of 12% simple interest?

A) $4,824.06
B) $4,828.66
C) $4,831.48
D) $4,837.87
E) $5,177.53