Question:
Why does it take 30 years to pay off a $150,000 loan, even though you pay $1,000 a month?
Loan Duration:
Financial institutions provide loans to customers to fulfill their needs, and customers pay back the loan with interest to a lender. Managers calculate the duration of a loan with the help of interest rate and principal amount.
Answer and Explanation:1
The interest rate on a loan directly affects the duration of a loan.
We will use monthly installment formula to calculate the interest rate:
{eq}\begin{align*}{\rm\text{Monthly Installment}} &= {\rm\text{Loan}} \times \dfrac{{{\rm\text{Interest Rate}}_{{\rm\text{Monthly}}}^{} \times \left( {1 + {\rm\text{Interest Rate}}_{{\rm\text{Monthly}}}^{}} \right)_{}^{{\rm\text{Years}} \times {\rm\text{Compounding}}}}}{{\left( {1 + {\rm\text{Interest Rate}}_{{\rm\text{Monthly}}}^{}} \right)_{}^{{\rm\text{Years}} \times {\rm\text{Compounding}}} - 1}}\\1,000 &= 150,000 \times \dfrac{{{\rm\text{Interest Rate}}_{{\rm\text{Monthly}}}^{} \times \left( {1 + {\rm\text{Interest Rate}}_{{\rm\text{Monthly}}}^{}} \right)_{}^{12 \times 30}}}{{\left( {1 + {\rm\text{Interest Rate}}_{{\rm\text{Monthly}}}^{}} \right)_{}^{12 \times 30} - 1}}\\0.0067 &= \dfrac{{{\rm\text{Interest Rate}}_{{\rm\text{Monthly}}}^{} \times \left( {1 + {\rm\text{Interest Rate}}_{{\rm\text{Monthly}}}^{}} \right)_{}^{360}}}{{\left( {1 + {\rm\text{Interest Rate}}_{{\rm\text{Monthly}}}^{}} \right)_{}^{360} - 1}}\\{\rm\text{Interest Rate}}_{{\rm\text{Monthly}}}^{} &= 0.585\% \\{\rm\text{Interest Rate}}_{{\rm\text{Annually}}}^{} &= 0.585\% \times 12\\&= 7.02\%\end{align*}{/eq}
Note: The interest rate is calculated using the hit and trial method.
Therefore, it takes 30 years to complete the loan of $150,000 with $1,000 per monthly installment at a 0.585% monthly interest rate.
