5. you took out student loans totalling $31,000 and have a repayment plan with the bank.\n a. what will your…
5. you took out student loans totalling $31,000 and have a repayment plan with the bank.\n a. what will your monthly payments be if the interest rate is 7% for 25 years?\nn = 25 x 12\ni% = 7\npv = 31000\npmt = ae\nfv = 0\npy = cy = 12\n b. what is the total amount you will pay over the 25 years?\n c. what amount will you pay in interest?
Answer
Explanation:
Step1: Calculate number of periods
$N = 25\times12=300$ (number of months in 25 years)
Step2: Determine monthly interest rate
$i=\frac{7%}{12}=\frac{0.07}{12}$
Step3: Use loan - payment formula
The formula for the present value of an ordinary annuity is $PV = PMT\times\frac{1-(1 + i)^{-N}}{i}$. Rearranging for $PMT$ gives $PMT=\frac{PV\times i}{1-(1 + i)^{-N}}$. Substituting $PV = 31000$, $i=\frac{0.07}{12}$, and $N = 300$: [ \begin{align*} PMT&=\frac{31000\times\frac{0.07}{12}}{1-(1+\frac{0.07}{12})^{-300}}\ &\approx219.10 \end{align*} ]
Step4: Calculate total amount paid in 25 years
$Total\ amount=PMT\times N$. Substituting $PMT = 219.10$ and $N = 300$, we get $Total\ amount=219.10\times300 = 65730$
Step5: Calculate total interest paid
$Interest\ paid=Total\ amount - PV$. Substituting $Total\ amount = 65730$ and $PV = 31000$, we get $Interest\ paid=65730 - 31000=34730$
Answer:
a. $$219.10$ b. $$65730$ c. $$34730$