# Suppose I have student loans totaling $10,000 and the interest rate is an annual percentage rate... ## Question: Suppose I have student loans totaling$10,000 and the interest rate is an annual percentage rate of 3.5%. The loan term is 10 years.

a) What will my monthly payments be?

b) How much will I pay over the lifetime of the loan?

## Annuity Payments:

A substantial loan amount taken upfront by a borrower from a lender is usually repaid by making relatively small equated monthly or quarterly payments over the tenor of loan. These periodic payments are called as annuity and each annuity consists of two components, namely, interest payment and principal repayment.

The number of monthly payments is given by:

{eq}\begin{align*} &= \text{Number of months per year * years till maturity} \\[0.3 cm] &= 12 * 10 \\[0.3 cm] &= 120 \end{align*} {/eq}

The monthly interest rate is given by:

{eq}\begin{align*} &= \dfrac{\text{Annual interest rate}}{\text{Number of months in a year}} \\[0.3 cm] &= \dfrac{3.5\%}{12} \\[0.3 cm] &= 0.2917\% \end{align*} {/eq}

The formula for monthly payment on loan is given as:

{eq}R\, = \dfrac{i}{1\, -\, \left ( 1\, +\, i \right )^{-n}}\times P {/eq}

Where;

R = monthly payment

i = interest rate = 0.2917%

P = Principal amount = $10,000 n = number of months = 120 months {eq}R\, = \dfrac{0.002917}{1\, -\, \left ( 1\, +\, 0.002917 \right )^{-120}}\times 10,000 {/eq} R {eq}= \$98.89 {/eq}

The total amount paid over the lifetime is given by:

{eq}\begin{align*} &= \text{Number of periods * Monthly payment} \\[0.3 cm] &= 120 * \$98.89 \\[0.3 cm] &= \$11,866.53 \end{align*} {/eq}