A company that manufactures purgable hydrogen sulfide monitors will make deposits such that each one is 4% larger than the preceding one. How large must the first deposit at the end of year 1 be if the deposits extend through year 10 and the 4th deposit is $6000?

1st deposit at the end of the 1st year = $5,547. 34 / (1.04) = $5,333.99

Explanation:

The question is on the first deposit at the end of the first year,

Step 1: one of the ways of calculating this is to begin the calculation from the known year which is the 4th year. Knowing the 4th year we can then calculate back to the first year.

4th year deposit = $6000

Formula for annual deposit = p / (1+r)

P = The deposit for the year of calculation = $6000

r = rate of yearly increase = 4%

Step 2: Apply the Formula as follows

4th deposit at the end of the 4th year = $6000

3rd deposit at the end of the 3rd year = $6,000 / (1.04) = $5,769.23

2nd deposit at the end of the 2nd year = $5,769.23 / (1.04) = $5,547.34

1st deposit at the end of the 1st year = $5,547. 34 / (1.04) = $5,333.99

However, if the calculations are too lengthy, you can use a formula to bypass calculating the individual years as follows

=P / (1+r) ∧n

Where number of years which in this case will be 4-1 = 3 (since we are looking for the first year).