Jeremy purchases a piece of construction equipment worth $26000 by paying 12% down and the balance with quarterly payments over 15 years at quarterly rate of 11% (i = 0.11/4). If he wants to refinance the loan, there is a penalty equal to one quarterly payment. If after 2 years he realizes he can borrow money from the bank at quarterly rate of 5% (i =0.05/4) . How much money does he save by refinancing?
I start off by finding the loan is $22880 (88% of 26000). Find the quarterly payment of the first rate
22880 = PMT(1-(1+.11/4)^-60/(.11/4)
PMT = 782.96 (rounded up)
Refinance by finding accum amount after 2 years and adding on the penalty:
22880(1+.11/4)^8 - 782.96(1+.11/4)^8-1/(.11/4) = 21524.78423.
Find the new quarterly payment using the new rate:
21524.78423 = PMT (1-(1+.05/4)^-52/(0.05/4)) = $565.4338 (565.44 rounded up)
Therefore he would've paid 782.96*60 = 46977.60, but he refinanced and paid 782.96*8 + 565.44*52 = 35666.56
Difference: 46977.6-35666.56 = 11311.04.
Can someone help with this question thanks
Here is how I would do it.
2 years in.
Loan balance $\$21,525$ Quarterly payment $\$783$
$5\%$ is the prevailing interest rate. The present value of the next 52 quarters of $\$783$ payments evaluated at the market rate is. $\$ 29,805$
Or pay $\$783$ penalty. Add that to the current loan balance, and you get $\$22,308$