his or her children or grandchildren, some of whom might have been looking after the borrower for many years. Conversely, in the unlikely event that the value of property had remained the same or reduced, the shared appreciation mortgage would have effectively been interest-free. Interest rate formula To calculate the equivalent compound interest rate of a "zero-interest" shared-appreciation mortgage, i.e. the rate of the interest that would have been charged once a month on the amount owing, and added to the amount owing, so that at the end of the term of the loan, the amount owing would be the same as the repayment owing on a shared-appreciation mortgage: which is the same as: where is the amount of the repayment, is the amount of the loan, and is the time in years (and part of a year) between the loan and the repayment. The formula gives the equivalent compound interest rate of the mortgage as a percentage. Alternatively, if it was assumed that the interest would have been charged once a year on the amount owing, and added to the amount owing, the formula would be: which is the same as: For loans that were 25% of the value of the property, the repayment would normally be 75% of the difference between the initial and final values of the property, plus the amount of the initial loan. The origin of shared appreciation mortgages There is a detailed account of the origin of shared appreciation mortgages in chapter 23 of Dr Bettina von Stamm's book Managing Innovation, Design and Creativity, first edition published in 2003 and second edition published in 2008. Chapter 23 is titled "Innovation in Financial Services, Case Study 8: Shared Appreciation Mortgage – Bank of Scotland". This is a précis of the chapter: The idea – rationale and getting buy-in Craig Corn, a director in structured finance at Merrill Lynch, was looking for a way to give investors access to one of the largest asset pools, the housing market. This was dominated by owner-occupiers, most of whose wealth was tied up in their homes. Meanwhile, commercial investment in the much smaller private rental sector of the market was hampered by the cost of managing rental property and the difficulty of gaining repossession. Linking an investment to a mortgage would give investors access to the much larger owner-occupier sector of the housing market and enable the owner-occupiers to