1. Mr Jones bought a building for $60,000, payable on the following terms: a $10,000 down...
1. Mr Jones bought a building for $60,000, payable on the following terms: a $10,000 down payment and 25 equal annual payments to include principal and interest of 10 percent per annum. Calculate the amount of the installment payments. How much of the first year's payment goes toward reducing the principal amount?
2. Crab the State Bank has offered you a $1,00,000 five- year loan at an interest of 11.25 percent, requiring equal annual end-of-year payments that include both principal and interest on the unpaid balance. Develop an amortization schedule for this loan.
Homework Answers
| Formula to calculate present value of annuity | |||||||
| Present value of annuity | Annuity amount*(1-((1+r)^-n)/r) | ||||||
| where r is interest rate and n is number of years | |||||||
| 1. | |||||||
| Using the present value of annuity formula we would calculate the annual payments under loan | |||||||
| Annual installment payment | (60000-10000)/[(1-(1.10^-25))/0.10] | ||||||
| Annual installment payment | 50000/9.07704 | ||||||
| Annual installment payment | $5,508.40 | ||||||
| Thus, annual installment payment would be $5,508.40 | |||||||
| Interest for first year | $5,000.00 | 50000*10% | |||||
| Principal payment | $508.40 | (5508.40-5000) | |||||
| Thus, in first year $508.40 would reduce the principal payment. | |||||||
| 2. | |||||||
| Calculation of annual installment payment | |||||||
| Annual installment payment | 100000/[(1-(1.1125^-5))/0.1125] | ||||||
| Annual installment payment | 100000/3.672771 | ||||||
| Annual installment payment | $27,227.40 | ||||||
| Amortization schedule for loan is shown below | |||||||
| Year | Beginning balance of loan | Total installment | Interest | Principal | Ending balance of loan | ||
| 1 | $100,000.00 | $27,227.40 | $11,250.00 | $15,977.40 | $84,022.60 | ||
| 2 | $84,022.60 | $27,227.40 | $9,452.54 | $17,774.85 | $66,247.75 | ||
| 3 | $66,247.75 | $27,227.40 | $7,452.87 | $19,774.53 | $46,473.22 | ||
| 4 | $46,473.22 | $27,227.40 | $5,228.24 | $21,999.16 | $24,474.06 | ||
| 5 | $24,474.06 | $27,227.40 | $2,753.33 | $24,474.06 | $0.00 | ||
| Interest = Beginning balance of loan*11.25% | |||||||
| Principal paid = Total installment amount - Interest paid | |||||||
| Ending balance of loan = Beginning balance - Principal paid | |||||||
| Beginning balance of loan is ending balance of previous year | |||||||
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