# John Dough has just been awarded his degree in business. He has three education loans...

## Question:

John Dough has just been awarded his degree in business. He has three education loans outstanding. They all mature in 5 years and can be repaid without penalty any time before maturity. The amounts owed on each loan and the annual interest rate associated with each loan are given in the following table:

Loan 1 $27,000 5.6% Loan 2$7,000 8.6%

Loan 3 $30,000 4.6% John can also combine the total of his three debts (that is,$64,000) and create a consolidated loan from his bank. His bank will charge an annual interest rate of 6.1% for a period of 5 years.

Should John do nothing (leave the three individual loans as is) or create a consolidated loan?

The weighted average annual interest rate on John's current loan portfolio is _____ %.

## Interest rate

The interest rate is a percentage that is charged by the financial institution for issuing the loan. It is charged on the principal amount of credits. Interest rates can be charged as a fixed rate and floating rate.

{eq}\begin{align*} \rm\text{Weighted average annual interest } &= \rm\text{ Interest rate } \times {\rm\text{ }}\dfrac{{{\rm\text{Loan 1}}}}{{{\rm\text{Total debt}}}} + {\rm\text{Interest rate }} \times {\rm{ }}\dfrac{{{\rm\text{Loan 2}}}}{{{\rm\text{Total debt}}}} + {\rm\text{Interest rate }} \times {\rm{ }}\dfrac{{{\rm\text{Loan 3}}}}{{{\rm\text{Total debt}}}}\\ & = 5.6\% \times \dfrac{{\$27,000}}{{\$ 64,000}} + 8.6\% \times \dfrac{{\$7,000}}{{\$ 64,000}} + 4.6\% \times \dfrac{{\$30,000}}{{\$ 64,000}}\\ & = 5.45\% \end{align*} {/eq}

John should not consolidate the loan as the weighted average annual interest rate is less than the rate offered by the bank.