Question

. In the provided scenario, you address the time value of money also known as discounted cash flow analysis. This type of analysis is crucial to being able to viably analyze financial statements.

The start-up firm you founded is trying to save $10,000 in order to buy a parcel of land for a proposed small warehouse expansion. In order to do so, your finance manager is authorized to make deposits of $1250 per year into the company account that is paying 12% annual interest. The last deposit will be less than $1250 if less is needed to reach $10,000.

o How many years will it take to reach the $10,000 goal and how large will the last deposit be? Show your work.

Answer 1

Answer:-

Total amount to accumulated = $ 10000
Early deposit = $ 1250 / year
Annual interest per year = 12 %
Let the final year deposit (payment) = $ X
The first year deposit and total amount = $ 1250 [ Every subsequent year the deposited amount will grow by 12 %]
The second year deposit plus total accumulated amount = $ 1250 + $ 1250 x (1.12) = $ 1250 + $ 1400 = $ 2650
The third year deposit plus total accumulated amount = $ 1250 + $ 2650 x (1.12) = $ 1250 + $ 2968 = $ 4218
The fourth year deposit plus total accumulated amount = $ 1250 + $ 4218 x (1.12) = $ 1250 + $ 4724.16 = $ 5974.16
The fifth year deposit plus total accumulated amount = $ 1250 + $ 5974.16 x (1.12) = $ 1250 + $ 6691.06 = $ 7941.06
The sixth year deposit plus total accumulated amount = $ X + $ 7941.06 x (1.12) = $ X + $ 8893.99
The last deposit plus accumulated deposit = $ 10000

$ X + $ 8894 = $ 10000
$ X = $ 10000 - $ 8894
$ X = $ 1106

The number of years required to reach the goal of $ 10000 is 6 years and the last deposit is equal to $ 1106