A loan is to be amortized every quarter by payments of P2,500.00 for 6 years. Money is worth 0.5% converted quarterly.14. How much is the original loan? Group of answer choicesP 59,072.57P 18,815.95P 68,746.96P 51,560.59

To find the original loan amount, we can use the formula for the present value of an ordinary annuity. The formula is:

P = PMT * [(1 - (1 + r)^-n) / r]

where: P = original loan amount PMT = periodic payment amount r = interest rate per period n = total number of payments

Given in the problem: PMT = P2,500.00 r = 0.5% per quarter = 0.005 n = 6 years * 4 quarters/year = 24 quarters

Substituting these values into the formula:

P = 2500 * [(1 - (1 + 0.005)^-24) / 0.005]

Calculating the above expression will give us the original loan amount.

Let's calculate it:

P = 2500 * [(1 - (1.005)^-24) / 0.005] P = 2500 * [(1 - 0.8899964482) / 0.005] P = 2500 * [0.1100035518 / 0.005] P = 2500 * 22.00071036 P = P55,001.7759

So, the original loan amount is approximately P55,001.7759. However, this value is not in the given options. There might be a mistake in the problem or in the given options.

To find the original loan amount, we can use the formula for the present value of an ordinary annuity. The formula is:

P = PMT * [(1 - (1 + r)^-n) / r]

where: PMT = periodic payment = P2,500 r = interest rate per period = 0.5% or 0.005 n = number of periods = 6 years * 4 quarters/year = 24 quarters

Substituting the given values into the formula, we get:

P = 2500 * [(1 - (1 + 0.005)^-24) / 0.005]

Solving this equation will give us the original loan amount.

Let's calculate it:

P = 2500 * [(1 - (1 + 0.005)^-24) / 0.005] P = 2500 * [(1 - 0.8899964482) / 0.005] P = 2500 * [0.1100035518 / 0.005] P = 2500 * 22.00071036 P = 55001.7759

So, the original loan amount is approximately P 55,001.78. However, this value is not in the provided options. There might be a mistake in the problem or the provided options.