*The balance after the third payment was $69,918.68. 10% of this amount is $6,991.87. **The balance after the fifth payment was $29,032.76. 10% of this amount is $2,903.28.
Step 2: Adjust for the “missing pennies” (noted in bold italics ) and total the interest.
0 | $0.00 | $118,000.00 | ||
1 | $18,000.00 | $2,278.41 | $15,721.59 | $102,278.41 |
2 | $18,000.00 | $86,253.25 | ||
3 | $24,991.87 | $62,926.81 | ||
4 | $18,000.00 | $1,215.02 | $16,784.98 | $46,141.83 |
5 | $20,903.28 | $890.93 | $20,012.35 | $26,129.48 |
6 | $18,000.00 | $8,634.01 | ||
7 | $8,800.72 | $166.71 | $8,634.01 | $0.00 |
Total |
From Question 18a, amount of interest paid was $9,391.27. Interest Saved = $9,391.27 − $8,695.87 = $695.40.
Step 1 : Find the initial payment.
[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 30 \times 12 = 360 \;\text{payments}[/latex] [latex]I/Y = 6.49[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV = 628,\!200 − 100,\!000 = 528,\!200[/latex] [latex]CPT\; PMT =-\$3,\!305.288742[/latex]
Make sure to reinput PMT = -3,305.29 (Input as a negative value rounded to 2 decimal places).
Step 2: Use the AMORT function to find the BAL on the after the first term (payment 1-36).
2nd AMORT P1 = 1 P2 = 36 ↓ BAL = $508,947.54
2nd AMORT P1 = 1 P2 = 36 ↓ ↓ PRN = $19,252.46 INT = $99,737.98
[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 27 \times 12 = 324 \;\text{payments}[/latex] [latex]I/Y = 6.19[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV = 508,\!947.54[/latex] [latex]CPT\; PMT =-\$3,\!211.32429[/latex]
Make sure to reinput PMT = -3,211.32 (Input as a negative value rounded to 2 decimal places).
Use the AMORT function to find the BAL on the after the second term (payment 1-48).
2nd AMORT P1 = 1 P2 = 48 ↓ BAL = $475,372.69
[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 20 \times 12 = 240 \;\text{payments}[/latex] [latex]I/Y = 4.84[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV = 323,\!000[/latex] [latex]CPT\; PMT =-\$2,\!094.701842[/latex]
Make sure to reinput PMT = -2,094.70 (Input as a negative value rounded to 2 decimal places).
Step 2: Use the AMORT function to find the BAL on the after the first 18 months.
2nd AMORT P1 = 1 P2 = 18 ↓ BAL = $308,009.80
Step 3: Find New Balance after $20,000 top-up payment.
New Balance = $308,009.80 − $20,000 = $288,009.80. Reinput PV = $288,009.80.
Step 4: Use the AMORT function to find the BAL on the after the last 18 months of the first term.
2nd AMORT P1 = 1 P2 = 18 ↓ BAL = $270,417.34
Step 1: Find Original BAL paid without top-up payment (payments 1-36).
Reinput PV = $323,000
2nd AMORT P1 = 1 P2 = 36 ↓ BAL = $291,904.76
Step 2: Find Interest Difference.
[latex]\begin{align} \text{Interest Difference}&=\$291,\!904.76 − \$270,\!417.34 − \$20,\!000\\ &= \$1,\!487.42 \end{align}[/latex]
Step 1 : Find the initial payment for 10-year term.
[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 30 \times 12 = 360 \;\text{payments}[/latex] [latex]I/Y = 7.7[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV = 408,\!650[/latex] [latex]CPT\; PMT =-\$2,\!879.565159[/latex]
Make sure to reinput PMT = -2,879.57 (Input as a negative value rounded to 2 decimal places).
Step 2: Use the AMORT function to find the BAL on the after the 10-year term (payments 1-120).
2nd AMORT P1 = 1 P2 = 120 ↓ BAL = $355,303.81
Step 3 : Find the payment for 5-year term.
[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 20 \times 12 = 240 \;\text{payments}[/latex] [latex]I/Y = 5.69[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV = 355,\!303.81[/latex] [latex]CPT\; PMT =-\$2,\!468.979621[/latex]
Make sure to reinput PMT = -2,468.98 (Input as a negative value rounded to 2 decimal places).
Step 4: Use the AMORT function to find the BAL on the after the 5-year term (payments 1-120).
2nd AMORT P1 = 1 P2 = 60 ↓ BAL = $299,756.24
Step 5 : Find the payment for 3-year term with amortization period shortened by 5 years. Number of years remaining = 15 – 5 = 10.
[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 10 \times 12 = 120 \;\text{payments}[/latex] [latex]I/Y = 3.45[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV =299,\!756.24[/latex] [latex]CPT\; PMT =-\$2,\!953.710318[/latex]
Make sure to reinput PMT = -2,953.71 (Input as a negative value rounded to 2 decimal places).
Step 6: Use the AMORT function to find the BAL on the after the 3-year term (payments 1-36).
2nd AMORT P1 = 1 P2 = 36 ↓ BAL = $220,328.74
Start of 3rd term principal = $299,756.24. Remaining balance at end of 3rd term = $220,328.74.
[latex]\begin{align} \text{Total principal across all}\;18\;\text{years}&=\$408,\!650 - \$220,\!328.74\\ &= \$188,\!321.26 \end{align}[/latex]
[latex]\text{Total interest across all}\;18\;\text{years}[/latex] [latex]=(120 \times 2,\!879.57) + (60 \times 2,\!468.98) + (36 \times 2,\!953.71) - 188,\!321.26[/latex] [latex]= \$411,\!499.50[/latex]
Figure 13.1.2: Timeline: Deferral period from age 54 until age 65 at 6.25% compounded annually. Starting at age 55, 20 years end of month payments of PMT at 3.85% compounded annually. $75,000 at age 54 brought to age 65 as FV. At age 65 the FV becomes the PV for the stream of PMT’s brought back to age 65. [ Back to Figure 13.1.2 ]
Business Math: A Step-by-Step Handbook Abridged Copyright © 2022 by Sanja Krajisnik; Carol Leppinen; and Jelena Loncar-Vines is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.
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