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Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.] a $100,000, 25-year, 4.3% mortgage after 10 years Step 1 Note that this question asks us to find the outstanding principal, after the first 10 years, on a 25-year, $100,000 mortgage. The present value formula can be used to calculate the outstanding principal on a mortgage, but to use this formula, the monthly payment on the mortgage must be known. To calculate the monthly payment PMT on a mortgage valued at PV dollars for n periods at an interest rate of i per period, use the formula PMT = PV The given mortgage is $100,000, so PV = 100000✔ The 4.3% annual interest rate as a decimal is 0.043, so the monthly interest rate is i = Step 2 With PV = 100,000, i = nearest cent. If the investment is for 25 years with monthly payments, then the number of pay periods is n = 25. 12 = 300✔✔ PMT= PV PV [1-(1²+1)-7] PMT= 100000 0.043 12 = 544.54 ✔ 100,000 100,000 544.54 0.043 0.043 12 1-(1+0.043-300 12 ✓ 12 and n = 300, we are now ready to find the monthly payment PMT, by substituting these known values into the formula. Simplify and round the result to the 300 i [1(1+1)

Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.] a $100,000, 25-year, 4.3% mortgage after 10 years Step 1 Note that this question asks us to find the outstanding principal, after the first 10 years, on a 25-year, $100,000 mortgage. The present value formula can be used to calculate the outstanding principal on a mortgage, but to use this formula, the monthly payment on the mortgage must be known. To calculate the monthly payment PMT on a mortgage valued at PV dollars for n periods at an interest rate of i per period, use the formula PMT = PV The given mortgage is $100,000, so PV = 100000✔ The 4.3% annual interest rate as a decimal is 0.043, so the monthly interest rate is i = Step 2 With PV = 100,000, i = nearest cent. If the investment is for 25 years with monthly payments, then the number of pay periods is n = 25. 12 = 300✔✔ PMT= PV PV [1-(1²+1)-7] PMT= 100000 0.043 12 = 544.54 ✔ 100,000 100,000 544.54 0.043 0.043 12 1-(1+0.043-300 12 ✓ 12 and n = 300, we are now ready to find the monthly payment PMT, by substituting these known values into the formula. Simplify and round the result to the 300 i [1(1+1)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.] a $100,000, 25-year, 4.3% mortgage after 10 years Step 1 Note that this question asks us to find the outstanding principal, after the first 10 years, on a 25-year, $100,000 mortgage. The present value formula can be used to calculate the outstanding principal on a mortgage, but to use this formula, the monthly payment on the mortgage must be known. To calculate the monthly payment PMT on a mortgage valued at PV dollars for n periods at an interest rate of i per period, use the formula PMT = PV The given mortgage is $100,000, so PV = 100000 The 4.3% annual interest rate as a decimal is 0.043, so the monthly interest rate is i = 12 Step 2 With PV = 100,000, i = If the investment is for 25 years with monthly payments, then the number of pay periods is n = 25. 12 = 300 nearest cent. PMT = PV PMT = = 1 − (1 + i)¯″¸ 100000 0.043 and n = "I 12 544.54 100,000 544.54 1 0.043 12 100,000 - (1 + 0.043 12 -300 0.043 300, we are now ready to find the monthly payment PMT, by substituting these known values into the formula. Simplify and round the result to the 12 Thus, the monthly payment on a 25-year, $100,000 mortgage at 4.3% per year is $544.54 300 544.54 1 − (1 + i)¯n¸
Transcribed Image Text:Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.] a $100,000, 25-year, 4.3% mortgage after 10 years Step 1 Note that this question asks us to find the outstanding principal, after the first 10 years, on a 25-year, $100,000 mortgage. The present value formula can be used to calculate the outstanding principal on a mortgage, but to use this formula, the monthly payment on the mortgage must be known. To calculate the monthly payment PMT on a mortgage valued at PV dollars for n periods at an interest rate of i per period, use the formula PMT = PV The given mortgage is $100,000, so PV = 100000 The 4.3% annual interest rate as a decimal is 0.043, so the monthly interest rate is i = 12 Step 2 With PV = 100,000, i = If the investment is for 25 years with monthly payments, then the number of pay periods is n = 25. 12 = 300 nearest cent. PMT = PV PMT = = 1 − (1 + i)¯″¸ 100000 0.043 and n = "I 12 544.54 100,000 544.54 1 0.043 12 100,000 - (1 + 0.043 12 -300 0.043 300, we are now ready to find the monthly payment PMT, by substituting these known values into the formula. Simplify and round the result to the 12 Thus, the monthly payment on a 25-year, $100,000 mortgage at 4.3% per year is $544.54 300 544.54 1 − (1 + i)¯n¸
Now that we have determined PMT = 544.54, we are ready to find the outstanding principal on the mortgage after 10 years. To calculate the outstanding principal PV of a loan amount, we use the present value formula. After k months there are n - k payments of PMT remaining to make. The outstanding principal 1 − (1 + i)−(n − k) - is the present value necessary to fund these payments. So, the outstanding principal = PV = PMT In the first 10 years of monthly payments, k = 10 - 12 = nk 300 120 = payments remaining. monthly payments are made. If there are n = 300 payments required over the course of 25 years, then there are
Transcribed Image Text:Now that we have determined PMT = 544.54, we are ready to find the outstanding principal on the mortgage after 10 years. To calculate the outstanding principal PV of a loan amount, we use the present value formula. After k months there are n - k payments of PMT remaining to make. The outstanding principal 1 − (1 + i)−(n − k) - is the present value necessary to fund these payments. So, the outstanding principal = PV = PMT In the first 10 years of monthly payments, k = 10 - 12 = nk 300 120 = payments remaining. monthly payments are made. If there are n = 300 payments required over the course of 25 years, then there are
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