Answer:
The answer is 2) an = 1000(1.018)n + 750n
Explanation:
The day their daughter was born, they deposited $1000 in an account that pays 1.8% compounded annually. This means thaht they have an interest of 1.8% of what they deposited each year.
To know how much interest is in a year, you must first know that 1.8% is the same as 0.018. This is obtained by dividing by 100, that is, you convert from percentage to decimal.
On the other side, what they deposited represents 100%. To convert it to decimal, it must be divided by 100, and it results in 1.
So, you want to know the total amount of money you have after a year, that is, what The Rickerts deposited added interest.
So, all this is represented as follows:
- 1000*100%(what The Rickerts deposited)+1000*1.8%(interest)
Converting the percentage to decimals:
So, to solve this, a common factor of 1000 will be taken::
But with this calculation you get interest after a year. You want to know the amount of money in the account n years after their daughter was born. For that you must multiply by the number of years of your daughter and you get: 1000*1.018*n
On the other hand,The Rickerts deposit an additional $750 into the account on each of her birthdays. On the first birthday, they deposit 750, on the second birthday 750, and so continuously every birthday. So, to know the amount they deposit on the nth birthday, multiply 750 by n: 750*n
Now, knowing finally both expressions, it is possible to know the total amount of money in the account n years after their daughter was born adding both expressions:
an=1000*1.018*n+750*n