Question

You plan to borrow $144,000 now and repay it in 25 equal annual installments (payments will be made at the beginning of each year). If the annual interest rate is 15%, how much will your annual payments be?

a. $3,586.99
b. $22,276.71
c. $4,374.38
d. $19,371.06
e. $27,177.59

Answer 1

b. $22,276.71

Step-by-step explanation:

From the given information:

using the basic time value of money function for PV of an annuity:

`PV = P \Bigg [ (1-(1+r)^(-n))/(r) \Bigg ]`

where;

P = annual Periodic Payment

r = rate per period = 15%

n = number of periods = 25

Present value PV = 144000

`144000= P \Bigg [ (1-(1+0.15)^(-25))/(0.15) \Bigg ]`

`144000= P \Bigg [ (1-(1.15)^(-25))/(0.15) \Bigg ]`

`144000= P \Bigg [ (1-0.0303776)/(0.15) \Bigg ]`

`144000= P \Bigg [ (0.9696224)/(0.15) \Bigg ]`

`144000= P \Bigg [6.464149333 \Bigg ]`

`P = (144000)/(6.464149333)`

P = $22276.71