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 outstanding principal,
R is the periodic payment,
r is the periodic interest rate, and
n is the number of remaining payments.

Given in the problem:
R = Php130,000 (the semi-annual payment),
r = 10% / 2 = 5% = 0.05 (the semi-annual interest rate), and
n = 9 * 2 - 8 * 2 = 2 (the number of remaining payments after 8 years).

Substituting these values into the formula gives:

P = Php130,000 * [1 - (1 + 0.05)^-2] / 0.05

Calculating the expression in the brackets first:

1 - (1 + 0.05)^-2 = 1 - 1.1025^-2 = 1 - 0.907029478 = 0.092970522

Then multiply by Php130,000 and divide by 0.05:

P = Php130,000 * 0.092970522 / 0.05 = Php243,502.58

So, the outstanding principal after the 8th year is Php243,502.58.

Question

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 outstanding principal,
R is the periodic payment,
r is the periodic interest rate, and
n is the number of remaining payments.

Given in the problem:
R = Php130,000 (the semi-annual payment),
r = 10% / 2 = 5% = 0.05 (the semi-annual interest rate), and
n = 9 * 2 - 8 * 2 = 2 (the number of remaining payments after 8 years).

Substituting these values into the formula gives:

P = Php130,000 * [1 - (1 + 0.05)^-2] / 0.05

Calculating the expression in the brackets first:

1 - (1 + 0.05)^-2 = 1 - 1.1025^-2 = 1 - 0.907029478 = 0.092970522

Then multiply by Php130,000 and divide by 0.05:

P = Php130,000 * 0.092970522 / 0.05 = Php243,502.58

So, the outstanding principal after the 8th year is Php243,502.58.

Knowee AI · Accepted Answer

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 outstanding principal,
R is the periodic payment,
r is the periodic interest rate, and
n is the number of remaining payments.

Given in the problem:
R = Php130,000 (the semi-annual payment),
r = 10% / 2 = 5% = 0.05 (the semi-annual interest rate), and
n = 9 * 2 - 8 * 2 = 2 (the number of remaining payments after 8 years).

Substituting these values into the formula gives:

P = Php130,000 * [1 - (1 + 0.05)^-2] / 0.05

Calculating the expression in the brackets first:

1 - (1 + 0.05)^-2 = 1 - 1.1025^-2 = 1 - 0.907029478 = 0.092970522

Then multiply by Php130,000 and divide by 0.05:

P = Php130,000 * 0.092970522 / 0.05 = Php243,502.58

So, the outstanding principal after the 8th year is Php243,502.58.

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 choicesPhp237,305.48Php233,047.20Php243,502.58Php241,723.36

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