4. [12] A reverse annuity mortgage is made with a balance not to exceed $300,000

Question

4. [12] A reverse annuity mortgage is made with a balance not to exceed $300,000 on a property now valued at $700,000. The loan calls for monthly payments to be made to the borrower for 120 months at an interest rate of 11% MEY. a. [3] What will the monthly payments be? b. [3] What will the RAM balance be at the end of year 3? c. [4] Assume that the borrower must have monthly draws of $2,000 for the first 50 months of the loan. The remaining draws from months 51 to 120 must be determined so that the $300,000 maximum is not exceeded in month 120. What will the draws by the borrower be during months 51 to 120? d. [2] Suppose property experiences a 1% appreciation (MEY, starting today), and the borrower has a balance of $300,000 at year 10 (by receiving payments computed in a). No payments are made thereafter. How many years from loan closing will the loan balance begin to exceed the house value?

Explanation / Answer

(a) Here in this problem the interest rate is 11% per annum and the period of annuity is 120 months. For making calculation for monthly payments we need to divide 115 by 12 to convert it to monthly rate. Also $300000 is an amount in future. Therefore: FV -300000 Time (in months) 120 Rate 11% Monthly payments 1382.500339 (b) What wiil be the RAM balance? The borrower will have collected the payments of $1382.50 for 3 years. We solve for the loan balance at the end of 36 months. Note that we are solving for FV as we want to know the RAM balance at the end of year 3. PMT -1382.5 rate 11% Time(in months) 36 Future Value 58649.9678 therefore RAM balance = $58649.9678 (c ) STEP-1 For getting the answer we have to find the FV of $2000 taken out every month for 50 months. PMT -2000 Rate 11% Time(in months) 50 Future value 126139.1028 STEP-2 We know that upto 50 months $126139.1 has been borrowed or taken out. Now we need to find out what is the balance amount at the end of 120 months on which we will have to calculate monthly instalments. For that first we need to find the future value of $126139.1 for 70 months at 11% per annum. PV -126139.1028 Rate 11% Time(in months) 70 Future value $238,920.02 Now the amount that is available against which withdrawals can be made = $61,079.98 Therefore, by taking 61080 as future value now we can calculate the PMT as: FV -61080 Time(in months) 70 rate 11% PMT $626.22 This is the required answer.

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