Question

Cal Lury owes $37,000 now. A lender will carry the debt for six more years at...

Cal Lury owes $37,000 now. A lender will carry the debt for six more years at 7 percent interest. That is, in this particular case, the amount owed will go up by 7 percent per year for six years. The lender then will require that Cal pay off the loan over the next 14 years at 10 percent interest. What will his annual payment be?

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Answer #1

Initial amount for consideration (P) = $37000

Rate of interest for 6 years (r) = 7%

Time (n) = 6 years

Amount owed after 6 years (A) = P * (1 + r)^n

Therefore, A = 37000 * (1.07)^6

A = 37000 * 1.501

A = 55,537

Now after six years,

rate of interest (r1) = 10%

time (n1) = 14 years

Let the amount (X) is paid at the end of each year (equal installments)

Please find the below table in excel showing year wise calculations. I have used Goal seek function under What If analysis in excel to obtain the value of X:

2 2 1i 30 1 8 2 393 531 3 46 2 519 0 0 95977 4216 3794 0 332211 94 94 94 94 94 94 94 94 94 94 94 94 94 94 088888888888888 75 75 75 75 75 75 75 75 75 75 75 75 75 75 3 86 6 31 1276732 13829 23142 616 012345678901 1 2 34567890123 22222223333 2 3

C24 22 Year B.Bal PymntInterest part Principal part Ending balance 23 0.00 1 61090.70 10000.00 2 56199.77 10000.00 3 50819.75 10000.00 4 44901.72 10000.00 5 38391.89 10000.00 6 31231.08 10000.00 7 23354.19 10000.00 8 14689.61 10000.00 5158.57 10000.00 5325.57 10000.00 11 -16858.13 10000.00 12-29543.94 10000.00 0.00 5553.70 5109.07 4619.98 4081.97 3490.17 2839.19 2123.11 1335.42 468.96 -484.14 1532.56 2685.81 13-43498.34 10000.00-3954.39 5349.83 0 55537.00 0.00 4446.30 4890.93 5380.02 5918.03 6509.83 7160.81 7876.89 8664.58 9531.04 10484.14 11532.56 12685.81 13954.39 15349.83 55537.00 51090.70 46199.77 40819.75 Goal Seek 34901.72 Set cell: 28391.89 To yalue: 21231.08 13354.19 25 27 2 2 SFS37 2 1 29 By changing cell: SCS24 4689.61 -4841.43 15325.57 26858.13 39543.94 53498.34 -68848.17 OK Cancel 10 3 37 1458848.17 10000.00

C25 22 YearB. Bal 23 24 25 PymntInterest part Principal part Ending balance 55537.00 53551.76 51368.00 48965.86 46323.51 0.00 1 61090.70 7538.94 2 58906.94 7538.94 3 56504.80 7538.94 4 53862.45 7538.94 550955.86 7538.94 6 47758.62 7538.94 7 44241.65 7538.94 8 40372. 7538.94 9 36117.44 7538.94 10 31436.36 7538.94 1126287.16 7538.94 12 20623.05 7538.94 13 14392.52 7538.94 14 7538.94 7538.94 0 55537.00 0.00 5553.70 5355.18 5136.80 4896.59 4632.35 4341.69 4021.97 3670.27 3283.40 2857.85 2389.74 1874.82 1308.41 685.36 0.00 1985.24 2183.76 2402.14 2642.35 2906.59 3197.25 3516.97 3868.67 4255.53 4681.09 5149.20 5664.12 6230.53 6853.58 Goal Seek Status 27 28 Goal Seeking with Cell F37 found a solution. 43416.92 40219.68 36702.71 32834.04 28578.51 23897.42 18748.22 13084.11 6853.58 -0.00 Target value: 0 Current value: -0.00 30 31 32 ок Cancel 35 37

As per the calculations shown in the above table, the annual payment comes out to be $7,538.94

Hope this answers your question.

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