Problem 4-78 (algorithmic) Question Help You owe your best friend $2,000. Becaus

Question

Problem 4-78 (algorithmic) Question Help You owe your best friend $2,000. Because you are short on cash, you offer to repay the loan over 10 months under the following condition. The first payment will be $90 at the end of month one. The second payment will be $90 G at the end of month two. At the end of month three, you'll repay $90 2G. This pattern of increasing G amounts will continue for all remaining months. a. what is the value of G if the interest rate is 0.5% per month? b. What is the equivalent uniform monthly payment? c. Repeat Part (a) when the first payment is S120 (i.e., determine G). Click the icon to view the interest and annuity table for discrete compounding when i:0.5% per month. a. The value of G is 15.1. (Round to the nearest cent.)

Explanation / Answer

Month 1 2 3 4 5 6 7 8 9 10 Payment 90 90 90 90 90 90 90 90 90 90 Additional Payment 1 2 3 4 5 6 7 8 9 Discount Factor 0.995025 0.990075 0.985149 0.980248 0.975371 0.970518 0.96569 0.960885 0.956105 0.951348 PV of payment 89.55224 89.10671 88.66339 88.22228 87.78336 87.34663 86.91207 86.47967 86.04942 85.62131 Sum 875.7371 PV of additional payment 0 0.990075 1.970298 2.940743 3.901483 4.85259 5.794138 6.726196 7.648837 8.562131 Sum 43.38649 a) G = 25.91 b) Equivalent Uniform Payment $205.54 c) Month 1 2 3 4 5 6 7 8 9 10 Payment 120 120 120 120 120 120 120 120 120 120 Additional Payment 1 2 3 4 5 6 7 8 9 Discount Factor 0.995025 0.990075 0.985149 0.980248 0.975371 0.970518 0.96569 0.960885 0.956105 0.951348 PV of payment 119.403 118.8089 118.2179 117.6297 117.0445 116.4622 115.8828 115.3062 114.7326 114.1618 Sum 1167.649 PV of additional payment 0 0.990075 1.970298 2.940743 3.901483 4.85259 5.794138 6.726196 7.648837 8.562131 Sum 43.38649 G = 19.18

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