What is the mortgage amount obtainable under the terms given, based on the monthly payment of $313?

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Multiple Choice

What is the mortgage amount obtainable under the terms given, based on the monthly payment of $313?

Explanation:
The amount you can borrow is found by treating the monthly payment as a level annuity and discounting those payments back to today at the loan’s interest rate and term. In other words, the loan amount is the present value of all future payments. Use the standard formula for a level-payment loan: L = PMT × [1 − (1 + i)^−n] / i, where: - PMT is the monthly payment (313), - i is the monthly interest rate (annual rate divided by 12), - n is the number of payments (years × 12). This calculation converts the stream of 313 payments into a single lump-sum loan amount today. Given the specified terms, that present value works out to about 58,306. So the mortgage amount obtainable under those terms with a monthly payment of 313 is 58,306; if the rate or term changed, the same payment would support a different loan amount.

The amount you can borrow is found by treating the monthly payment as a level annuity and discounting those payments back to today at the loan’s interest rate and term. In other words, the loan amount is the present value of all future payments.

Use the standard formula for a level-payment loan: L = PMT × [1 − (1 + i)^−n] / i, where:

  • PMT is the monthly payment (313),

  • i is the monthly interest rate (annual rate divided by 12),

  • n is the number of payments (years × 12).

This calculation converts the stream of 313 payments into a single lump-sum loan amount today. Given the specified terms, that present value works out to about 58,306. So the mortgage amount obtainable under those terms with a monthly payment of 313 is 58,306; if the rate or term changed, the same payment would support a different loan amount.

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