# Loan Payment Problems

At the beginning of the year you take out a loan of $60,000 at 12% annual interest rate compounded monthly. The minimum monthly payment on the first day of each month is 3% of the amount owed or $10, whichever is greater. You may assume that a year is evenly divided into 12 months.

(1) Suppose you make 11 minimum monthly payment and then pay off the entire loan on the last day of the year. What is the amount of your last payment?

(2) Suppose that you always make minimum monthly payments, at what time will your payment decrease to $10?

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#### Solution Preview

Please see attached Excel file for solution.

Loan Amount $60,000.00

Interest Rate 12% compounded monthly

Month Min. Payment Principal

0 $- $60,000.00

1 $1,800.00 $58,200.00

2 $1,746.00 $56,454.00

3 $1,693.62 $54,760.38

4 $1,642.81 $53,117.57

5 $1,593.53 $51,524.04

6 $1,545.72 $49,978.32

7 $1,499.35 $48,478.97

8 $1,454.37 $47,024.60

9 $1,410.74 $45,613.86

10 $1,368.42 $44,245.45

11 $1,327.36 $42,918.08

12

Month Min. Payment Principal

0 $- $60,000.00

1 $1,800.000 $58,200.00

2 $1,746.000 $56,454.00

3 $1,693.620 $54,760.38

4 $1,642.811 $53,117.57

5 $1,593.527 $51,524.04

6 $1,545.721 $49,978.32

7 $1,499.350 $48,478.97

8 $1,454.369 $47,024.60

9 $1,410.738 $45,613.86

10 $1,368.416 $44,245.45

11 $1,327.363 $42,918.08

12 $1,287.543 $41,630.54

13 $1,248.916 $40,381.63

14 $1,211.449 $39,170.18

15 $1,175.105 $37,995.07

16 $1,139.852 $36,855.22

17 $1,105.657 $35,749.56

18 $1,072.487 $34,677.08

19 $1,040.312 $33,636.76

20 $1,009.103 $32,627.66

21 $978.830 $31,648.83

22 $949.465 $30,699.37

23 $920.981 $29,778.38

24 $893.352 $28,885.03

25 $866.551 $28,018.48

26 $840.554 $27,177.93

27 $815.338 $26,362.59

28 $790.878 $25,571.71

29 $767.151 $24,804.56

30 $744.137 $24,060.42 ...

#### Solution Summary

This solution helps answer questions about loan payment.