A loan is to be amortized via equal payments of Php130,000 at the end of 6 months for 9 years. If the interest is 10% compounded semi-annually, find the outstanding principal after the 8th year.Group of answer choicesPhp241,723.36Php233,047.20Php243,502.58Php237,305.48
Question
A loan is to be amortized via equal payments of Php130,000 at the end of 6 months for 9 years. If the interest is 10% compounded semi-annually, find the outstanding principal after the 8th year.Group of answer choicesPhp241,723.36Php233,047.20Php243,502.58Php237,305.48
Solution
To solve this problem, we need to use the formula for the outstanding balance of an amortizing loan, which is:
P = R * [1 - (1 + r)^-n] / r
Where: P is the principal amount of the loan, R is the periodic payment, r is the periodic interest rate, and n is the number of payments made.
Given: R = Php130,000 (the semi-annual payment), r = 10%/2 = 5% = 0.05 (the semi-annual interest rate), n = 8*2 = 16 (the number of payments made in 8 years).
Substituting these values into the formula, we get:
P = Php130,000 * [1 - (1 + 0.05)^-16] / 0.05
Solving this equation will give us the outstanding principal after the 8th year.
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