A bank has an account for investors. Interest is added to the acc at the end of each year at a fixed rate of 5% of the amt in the account at the beginning of that year. A man decides to invest $x at the beginning of one year and then a further $x at the beginning of the second and each subsequent year. He also decides that he will not draw any money out of the account, but just leave it, and any interest to build up. Let the amount of money in his bank account at the end of t years be denoted by m. Show that the rate of change of the investment per year is given by 0.05(m+21x)

Solve by DE.

Question

A bank has an account for investors. Interest is added to the acc at the end of each year at a fixed rate of 5% of the amt in the account at the beginning of that year. A man decides to invest $x at the beginning of one year and then a further $x at the beginning of the second and each subsequent year. He also decides that he will not draw any money out of the account, but just leave it, and any interest to build up. Let the amount of money in his bank account at the end of t years be denoted by m. Show that the rate of change of the investment per year is given by 0.05(m+21x)

Solve by DE.