Question

Question 1.

Determine the future worth in year 10 of a cash flow series that starts in year 0 (today) at $25,000 and decreases by 6% per year (through year 10). Use an interest rate of 6%.

Question 2.

Person opens a savings account today. In year 1, she deposited $5,000. She made no deposits in year 2 and 3 and then deposit $2,000 each for years 4 trough 6. Given an interest rate of 4%, how much would she have needed to deposit each year if she made expial payments in years 1 through 6 to have the same amount in the account at the end of year 6?

Answer 1

Question 1.

Here, as per the question in the year 0 person has deposited $25,000 and than she is depositing the money till year 10. The deposits has reduced by 6% every year. So, his deposits will be:-

Year 0 - 25000

Year 1 - 23500 (25000 - 25000(6%)

Year 2 - 22090 (23500 - 23500(6%)

and so on till year 10.

So, future worth in year 10 will be:-

= 25000 (1.06^11) + 23500 (1.06^10) + 22090 (1.06^9) + 20764.6 (1.06^8) + 19518.724 (1.06^7) + 18347.6 (1.06^6) + 17246.74 (1.06^5) + 16211.94 (1.06^4) + 15239.22 (1.06^3) + 14324.87 (1.06^2) + 13465.38 (1.06)

= 14273.30+16095.42+18150+20467+23080+26026+29349+33096+37320+42085+47457

= $ 307,398.72

Question 2,

Firts of all, let us calculate what she will have at the end of year 6 with the current deposit scheme.

Year 0 - 0

Year 1 - 5000

Year 2 and 3 - 0

Year 4 to 6 - 2000

= 5000 (1.04^6) + 2000 (1.04^3) + 2000 (1.04^2) + 2000 (1.04)

= 6326.59 + 2249.73 + 2163.2 + 2080

= 12819.52

Now, if the person wants the same amount at the end of year 6, he has to deposit the following each year:-

12819.52 = Present value of future cash flow each year

= if the person deposits 2000 each year the future cash flow at 4% will be+

= 2000 (1.04^6) + ...... 2000 (1.04)

= 2530.63 + 2433.30 + 2339.71 + 2249.728 + 2163. 2 + 2080

= 13796.57

So, if at $ 2000, future cash flow is 13796.57, for future cash flow of 12819.52, the value will be,

= (2000*12819.52)/13796.57

= $ 1858.36.