# Customer opens an account in which the end of each month \$1000 is deposited. How much money will be accumulated after 7 years if the bank's interest rate is 4.5% per year? The annual rate of interest of the account is 4.5%. It is not given if the interest is compounded every month or once in a year. Assuming that interest is compounded every month, the interest rate for a month is `0.045/12 = 0.00375` .

The total tenure is 7*12 =...

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The annual rate of interest of the account is 4.5%. It is not given if the interest is compounded every month or once in a year. Assuming that interest is compounded every month, the interest rate for a month is `0.045/12 = 0.00375` .

The total tenure is 7*12 = 84 months.

The money accumulated at the end of 7 years is equal to:

`1000*(1.00375)^84 + 1000*(1.00375)^83 +...+ 1000`

This is geometric series that has a sum:

`1000*(1.00375^84 - 1)/(1.00375 - 1)`

=> `1000*98.5206`

=> 98520.6

The amount accumulated after 7 years in the account is \$98520.6

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