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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

Respuesta :

ajeigbeibraheem

Answer:

b. $22,276.71

Explanation:

From the given information:

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

[tex]PV = P \Bigg [ \dfrac{1-(1+r)^{-n}}{r} \Bigg ][/tex]

where;

P = annual Periodic Payment

r = rate per period  = 15%

n = number of periods = 25

Present value PV = 144000

[tex]144000= P \Bigg [ \dfrac{1-(1+0.15)^{-25}}{0.15} \Bigg ][/tex]

[tex]144000= P \Bigg [ \dfrac{1-(1.15)^{-25}}{0.15} \Bigg ][/tex]

[tex]144000= P \Bigg [ \dfrac{1-0.0303776}{0.15} \Bigg ][/tex]

[tex]144000= P \Bigg [ \dfrac{0.9696224}{0.15} \Bigg ][/tex]

[tex]144000= P \Bigg [6.464149333 \Bigg ][/tex]

[tex]P = \dfrac{144000}{6.464149333}[/tex]

P = $22276.71

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