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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

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

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. ¡ P√ [₁=(₁^²+0²"] ¸1 − (1 + i)¯n¸ To calculate the monthly payment PMT on a mortgage valued at PV dollars for n periods at an int est rate of i per period, use the formula PMT = PV| The given mortgage is $100,000, so PV = 100000 100,000 The 4.3% annual interest rate as a decimal is 0.043, so the monthly interest rate is i = 12 0.043 12 If the investment is for 25 years with monthly payments, then the number of pay periods is n = 25. 12 = 300 300
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. ¡ P√ [₁=(₁^²+0²"] ¸1 − (1 + i)¯n¸ To calculate the monthly payment PMT on a mortgage valued at PV dollars for n periods at an int est rate of i per period, use the formula PMT = PV| The given mortgage is $100,000, so PV = 100000 100,000 The 4.3% annual interest rate as a decimal is 0.043, so the monthly interest rate is i = 12 0.043 12 If the investment is for 25 years with monthly payments, then the number of pay periods is n = 25. 12 = 300 300
With PV = 100,000, i = nearest cent. PMT = PV PMT = 1 100000 = 1048 0.043 12 i -n (1 + i)¬^ 1 I 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 0.043 12 1 + 0.043 12 -300 X Thus, the monthly payment on a 25-year, $100,000 mortgage at 4.3% per year is $ 1048 X
Transcribed Image Text:With PV = 100,000, i = nearest cent. PMT = PV PMT = 1 100000 = 1048 0.043 12 i -n (1 + i)¬^ 1 I 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 0.043 12 1 + 0.043 12 -300 X Thus, the monthly payment on a 25-year, $100,000 mortgage at 4.3% per year is $ 1048 X
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