Question

Emma Jarmel obtained a $6,000 loan at 10% for home improvements. The monthly payment is $276.60 What is the amount of the a) interest for the first payment, b) payment to principal, and c) new principal?

Answer 1

The simple interest is given by

$\begin{gathered} \text{Interest}=\text{ Principal}\times\text{ Rate}\times\text{ Time} \\ \text{Interest}=\text{ 6000}\times\text{ 0.1}\times\frac{1}{12} \\ \text{Interest}=\text{ }50 \end{gathered}$

Therefore, the amount of the interest was $50.

Lets find the payment to the principal.

$\begin{gathered} \text{ Payment to the principal = Monthly Payment - Interest} \\ \text{ Payment to the principal =}276.60-50 \\ \text{ Payment to the principal =}226.60 \end{gathered}$

Then, her paymento to principal was $226.60

Finally, lets find the new principal.

$\begin{gathered} \text{ New principal = Previous principal - Payment to principal} \\ \text{ New principal = }6000-226.60 \\ \text{ New principal = }5773.40 \end{gathered}$

Then, Emma's new principal was $5773.40.