Kay has just taken out a $200,000, 30-year, 5%, mortgage. She has heard from fri
ID: 2693609 • Letter: K
Question
Kay has just taken out a $200,000, 30-year, 5%, mortgage. She has heard from friends that if she increases the size of her monthly payment by one-twelfth of the monthly payment, she will be able to pay off the loan much earlier and save a bundle on interest costs. She is not convinced. Use the necessary calculations to help convince her that this is in fact true. I got the minimum TVM, but not the maximin TVM input keys for the financial calculator... Also, I need a written out calculation for the whole problemExplanation / Answer
We first solve for the required minimum monthly payment: PV = $200,000; I/Y=5; N=30 x 12=360; FV=0; C/Y=12; P/Y=12; PMT = $1,073.64 Next, we calculate the number of payments required to pay off the loan, if the monthly payment is increased by 1/12 x $1073.64, that is by $89.47 PMT = 1163.11; PV=$200,000; FV=0; I/Y=5; C/Y=12; P/Y=12; Compute N = 303.13 months or 303.13/12 = 25.26 yearsHow much did you save by adding 1/12th to each payment? With minimum monthly payments: Total paid = 360 x $1073.64 = $386, 510.40 Minus Amount borrowed - $200,000.00 Interest paid = $186,510.40 With higher monthly payments: Total paid = 303.13 x $1163.11 = $353,573.53 Minus Amount borrowed - $200,000.00The nominal risk-free rate is the rate of interest earned on a risk-free investment such as a bank CD or a treasury security. It is essentially a compensation paid for the giving up of current consumption by the investor The real rate of interest adjusts for the erosion of purchasing power caused by inflation. The Fisher Effect shown below is the equation that shows the relationship between the real rate (r*), the inflation rate (h), and the nominal interest rate (r): (1 + r) = (1 + r*) x (1 + h) r = (1 + r*) x (1 + h) – 1 r = r* + h + (r* x h)
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