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The amount applied to the principal balance is $1174.43.We first calculate the Equated Monthly Instalment (EMI) of the loan by using the following formula:where r = Interest rate per period ; n = number of periodsSubstituting these in the formula above we get,Solving we get,Once we get the EMI, we calculate the amount that applies to the principal balance as follows:Interest is calculated on the outstanding balance of each month. In the first month, the entire principal in outstanding. Hence we...

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taytaycola223

05.07.2022

Business

The amount applied to the principal balance is $1174.43.

We first calculate the Equated Monthly Instalment (EMI) of the loan by using the following formula:

$\mathbf{PV = EMI * \left [\frac{1-(1+r)^{-n}}{r} \right]}$

where

r = Interest rate per period ; n = number of periods

$r = \frac{0.0425}{12}$

n = 15 * 12 = 180

Substituting these in the formula above we get,

$\mathbf{295000 = EMI * \left [\frac{1-(1+\frac{0.0425}{12})^{-180}}{\frac{0.0425}{12}}\right]}$

Solving we get,

$\mathbf{295000 = EMI * 132.9295092}$

$\mathbf{EMI = \frac{295000}{132.9295092}}$

$\mathbf{EMI = 2219.221313}$

Once we get the EMI, we calculate the amount that applies to the principal balance as follows:

Interest is calculated on the outstanding balance of each month. In the first month, the entire principal in outstanding. Hence we calculate interest on $295,000.

$\mathbf{Interest = 295000 * 0.003541667 = 1044.791667}$

$\mathbf{Amount applied to principal = EMI - Interest in dollars}$

$\mathbf{Amount applied to principal = 2219.221313 - 1044.791667 = 1174.429646}$

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