Question

Loan payment:   Determine the​ equal, annual,​ end-of-year payment required each year over the life of the loan shown in the following table to repay it fully during the stated term of the loan.  ​(Click on the icon located on the​ top-right corner of the data table below in order to copy its contents into a​ spreadsheet.)

Loan: Principal: Interest rate: Term of loan (years):

A $12,000 8%    3

B $60,000 12% 10

C $75,000 10%    30

D $4,000 15%    5

Answer 1

Annual Payment = (r x P)/[1-(1+r)-n]

P = Principal of loan

r = Rate of interest

n = Number of periods

A.

P = $ 12,000; r = 8 %; n = 3

Annual payment = (0.08 x $ 12,000) / [1 – (1+0.08) -3]       

                              = $ 960 / [1 – (1.08) -3]

                              = $ 960/ (1 – 0.79383224102017)

                               = $ 960/0.20616775897983

                               = $ 4,656.4021685559 or $ 4,656.40

B.

P = $ 60,000; r = 12 %; n = 10

Annual payment = (0.12 x $ 60,000) / [1 – (1+0.12) -10]       

                              = $ 7,200 / [1 – (1.12) -10]

                              = $ 7,200 / (1 – 0.3219732365907)

                               = $ 7,200 /0.6780267634093

                               = $ 10,619.0498495906 or $ 10,619.05

C.

P = $ 75,000; r = 10 %; n = 30

Annual payment = (0.1 x $ 75,000) / [1 – (1+0.1) -30]       

                              = $ 7,500 / [1 – (1.1) -30]

                              = $ 75200 / (1 – 0.05730855330117)

                               = $ 7,500 / 0.94269144669883

                               = $ 7,955.9436189475 or $ 7,955.94

D.

P = $ 4,000; r = 15 %; n = 5

Annual payment = (0.15 x $ 4,000) / [1 – (1+0.15) -5]       

                              = $ 600 / [1 – (1.15) -5]

                              = $ 600 / (1 – 0.49717673529829)

                               = $ 600 / 0.50282326470171

                               = $ 1,193.2622098461 or $ 1,193.26