We receive a mortgage loan of $200,000 for 20 years.. The mortgage rate is 12% p
ID: 2653217 • Letter: W
Question
We receive a mortgage loan of $200,000 for 20 years.. The mortgage rate is 12% per annum. First, derive the monthly payment we ought to make to the bank to amortize the loan. Secondly, compute the remaining amount we still owe the bank, if we pay an additional single sum of $40,000 after 4years. Thirdly, as part of this computation find how many more months, we will pay the bank to induce the loan expire. Fourthly, if we accumulate a lot by year 10(end of the year), how much would we give additionally to the lender to eliminate the loan?
Please only use the attached formula, dont use excel formulas.
Explanation / Answer
Mortgage Loan Amount = 200000
Term of Loan = 20 Year = 20*12 = 240 Months
Mortgage Interest rate = 12% per annuam
Monthly interest rate = 12%/12 = 1%
Using Excel formula
1)
Monthly Payment = pmt(rate,nper,pv,fv)
rate (monthly rate) = 1%
nper (no of month) = 240
pv (loan amount) = 200000
FV (Loan payable at the end of term) = 0
Monthly Payment = pmt(1%,240,-200000,0)
Monthly Payment = $ 2202.17
2)
Remaining Amount after 4 year after additional single sum of $40,000 payment = pv(rate,nper,pmt,fv) - 40000
rate (monthly rate) = 1%
nper (no of month left after 4 year) = 240 - 4*12 = 192
pmt (Monthly Payment ) = 2202.17
FV (Loan payable at the end of term) = 0
Remaining Amount after 4 year after additional single sum of $40,000 payment = pv(1%,192,-2202.17,0) - 40000
Remaining Amount after 4 year after additional single sum of $40,000 payment = $ 147,622.29
3)
No of month more required to pay the Remaining Amount = nper(rate,pmt,pv,fv)
rate (monthly rate) = 1%
pmt (Monthly Payment ) = 2202.17
PV (loan outstanding after 4 year after 40000payment) = 147622.29
FV (Loan payable at the end of term) = 0
No of month more required to pay the Remaining Amount = nper(1%,2202.17,-147622.29,0)
No of month more required to pay the Remaining Amount = 111.53 Months
4)
If we dont pay till year 10 and accumulated and we give additionally to the lender to eliminate the loan
Additionally to the lender to eliminate the loan = 200000*(1+12%)^20 - 200000
Additionally to the lender to eliminate the loan = $1,729,258.62
Note: The formulas you have given are not clear and thus, solved in excel.
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