On January 1, 2017, Crane Company decided to begin accumulating a fund for asset replacement five years later. The company plans to make five annual deposits of $64000 at 10% each January 1 beginning in 2017. What will be the balance in the fund, on January 1, 2022 (one year after the last deposit)

Balance in the account on January 1, 2022 =$820,525.44

Explanation:

Ordinary annuity is that in which the annual cash flow occurs at the end of each year for certain number of years.

Where the cash flow occurs at the beginning of the period, it is known as annuity due. The deposit scheme decided by Crane Company is annuity due, so we would need to work out the future value of an annuity due as follows:

Future Value of Annuity Due (FVAD): This represents the total sum that would accrue where the annual cash flow( each occurring at the beginning of the year) is compounded at a particular rate. It can be determined as

FV = A×( (1+r)^n - 1)/r)× (1+r)

This is the same formula as the ordinary annuity but with an additional provision for the the first cash flow to earn interest. This is effected by multiplying the ordinary annuity formula with (1+r)

Now, we can apply this formula to our question:

DATA

A-cash flow- 64,000

r- discount rate-10%

n-number of years- 5

FV = 64,000 × ( 1.1^5 - 1)/0.05  × 1.05 =  820,525.44  

FV = 820,525.44

Balance in the account on January 1, 2022 =820,525.44

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