Question

A widow wishes to take out a reverse mortgage on her house. What annual payment can she get if she decides on a $100,000 debt at the end of 10 years, the current rate is 9%, and she wants to take a $10,000 advance?

Answer 1

Step-1, Calculation of Future Value of $10,000 after 10 years at 9% Interest Rate

Future Value = Advance Amount x (1 + r)ⁿ

= $10,000 x (1 + 0.09)¹⁰

= $10,000 x 2.367363

= $23,674

Step-2, The Amount available for annuity payment

The Amount available for annuity payment = Debt – Future Value of Advance payment

= $10,000 - $23,674

= $76,326

Step-3, Calculation of the Annual Payment that she would get

Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r ]

Future Value = $76,326

Interest Rate (r) = 9%

Number of period = 10 Years

Annual Payment (P) = ?

Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r ]

$76,326 = P x [{(1 + 0.09)¹⁰ – 1} / 0.09]

$76,326 = P x [(2.36736 – 1 ) / 0.09]

$76,326 = P x [2.36736 / 0.09]

$76,326 = P x 15.19293

P = $76,326 / 15.19293

P = $5,024 per year

“Therefore, she would get annual payment of $5,024 per year”