Question

A debt of $5,000 can be repaid, with interest of 12%, by the following schedule: (year1) $500; (year2) $1,000; (year3) $1,000; (year4) $ X; (year5) $2080. To the nearest $, what is X?

A.

$2934

B.

$2954

C.

$2834

D.

$3934

Answer 1

Rate of Interest 12%

Present value of a payment can be calculated as: Payment / (1 + rate of interest)^^Year

Present value of payment made after 1 year is 500 / (1 + 0.12)^¹ = 446.43

Present value of payment made after 2 year is 1,000 / (1 + 0.12)^² = 797.19

Present value of payment made after 3 year is 1,000 / (1 + 0.12)^³ = 711.78

Present value of payment made after 3 year is X / (1 + 0.12)^⁴ = 0.64X

Present value of payment made after 5 year is 2,080 / (1 + 0.12)^¹⁵ = 1,180.25

Sum of present value in these 5 years should be 5,000: 0.64X + 3,135.65 = 5,000

X = 2,934

Option A is correct.