# Amount of the Equal Annual Deposit

Astros Co wants to accumulate $2,000,000 by 10/1/10. To achieve this goal, Astros Co will make the first of 6 equal annual deposits on 10/1/05. The deposits will be placed into a fund that earns interest at 10%

**Compute the:

1) amount of the equal annual deposit

2) balance of the account at 10/1/08, immediately after the 4th deposit

3) amount of increase in the balance of the account from 10/1/07 to 10/1/08

4) amount of interest earned from 10/1/06 through 10/1/08

On 10/1/08, after making 4 deposits for the amount determined in (1), Astros Co discovers that the amount needed will be $1,500,000 instead of $2,000,000. However, the $1,500,000 will not be needed until 10/1/13. So, Astros Co will not be required to make the remaining 2 deposits computed in (1) and instead will be allowed to make a single withdrawal on 10/1/11

**Compute the:

5) balance of the account on 10/1/10

6) amount of the withdrawal made on 10/1/11

7) amount of interest earned from 10/1/10 through 10/1/12

CLUE MUST MATCH:::The balance in the account at 10/1/07, immediately after the third deposit, is approximately $858,002.

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#### Solution Preview

**Compute the:

1) amount of the equal annual deposit

2) balance of the account at 10/1/08, immediately after the 4th deposit

3) amount of increase in the balance of the account from 10/1/07 to 10/1/08

4) amount of interest earned from 10/1/06 through 10/1/08

1. The amount of equal deposit can be found by finding the annuity value which grows to $2,000,000 in 6 years at 10% interest. Use the FVIFA table and get the factor. This is 7.716. Divide the amount by this factor to get the annual deposit. This comes to $259,201.7.

2. To find the balance, we need to find the values of the remaining deposits. ...

#### Solution Summary

The solution has problems relating to calculating the annuity amount, amount of interest earned and the balance in the account. The amount of increase in the balance of the account is determined.