Question 567610: Assume your planning to invest $5000 each year for 6 years earning 10% per year. What is the future value in the first $5000 invested?
Please help solve future value in the first $5000 invested.
Here is what I've thus far:
Future Value = present value X [(1 + interest rate) x (number of years)]
FV= $5000 x (1 + .010 x 6)
FV = $5000 x 1.010 x 6)
FV = $5000 x 6.06
FV = $30,300
30,300 - 30,000 = 300.00 / 6 = $50.00
First year $5000 investment is worth 5,050.00
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The basic question is that if you invest $5000 at an annual interest rate of 10 percent, what will that investment be worth at the end of 6 years? This presumes that you let the $5000 stay invested for the full 6 years and that all annual dividends stay invested and draw interest also.
.
That being the case, the general formula for calculating such a future value is:
.
.
And the variables are defined as follows:
.
P = Future Value
C = Initial Deposit
R = Annual Interest Rate expressed as a decimal (example 6% = 0.06)
N = The number of times per year the interest is compounded
T = The number of years that the initial deposit remains invested
.
For this problem you are to solve for P, the Future Value. C the Initial Deposit is $5000. R the Annual Interest Rate is 10% or 0.10. N is the number of times per year that the interest is calculated. Although the problem doesn't say so directly, it appears that the interest is awarded at the end of each year. That being the case, N equals 1 for one time per year. And finally, T is the number of years that the $5000 remains invested, which in this case is 6 full years.
.
Substitute these values into the general equation and it becomes:
.
.
which when you account for the fact that N = 1, simplifies to:
.
.
Combining the two terms in the parentheses reduces the equation to:
.
.
If you raise 1.1 to the 6th power (the same as multiplying 1.1 times itself six times) using a calculator you get 1.771561. Substituting this into the equation you now have:
.
.
Using a calculator to multiply out the right side gives you the answer:
.
.
which rounds off to an answer of:
.
 or P = $8,857.81
.
What you are doing by using this formula is to recognize that after the first year, you get 10% interest on your $5000 investment. (10% of $5000 is $500.) So at the end of the first year, you will have a total of $5500 in the bank. That stays invested so at the end of the second year, you get 10% of that or $550 in interest. That added to the $5500 that was in your account for the second year means that at the end of the second year you have $6050 in your account which remains invested during the entire third year. At the end of the third year the $6050 draws $605 in interest. This added to the $6050 results in your account at the end of the third year being $6050 + $605 = $6655. In the fourth year the $6655 is invested at 10% and so it earns $665.50 of interest. Adding that to the $6655 you had invested during the year gives you a total of $6655 + $665.50 which, at the end of the fourth years gives you $7320.50. During the fifth year the $7320.50 earns 10% interest. That means that at the end of the fifth year you add interest of $732.05 to the $7320.50 in your account to get a total amount of $8052.55. This amount remains invested throughout the sixth year so that at the end of the sixth year, 10% interest amounts to $805.255 which is then added to the $8052.55 resulting in a total of $8857.805. Note that this agrees exactly with the Future Value that we got by using the formula, and it checks out our answer.
.
Write down the future value equation and the definition of all its variables. It's likely that you will be able to use this formula again in similar problems.
.
Note that 10% converts to 0.10 in decimal form, not to 0.01 as you indicated in your work. And also note that if you had multiplied 1.1 times 6 you would have gotten a future value of $33,000. This is way too high. I'm not sure why you then divided that future value by 6, but if you did the answer would have been $5,500 which is too low when compared to the answer of $8857.81.
.
You can always approximate the answer by multiplying the annual percentage rate times the number of whole years. Then take that answer and multiply it by the original investment. That will give you only an approximate amount of interest earned over the 6 years of investment and you add that to the original investment. In this case 10% or 0.1 times 6 years = 0.6. Multiply that by the original investment of $5,000 and it tells you that the $5,000 will earn $3,000 in 6 years. So at the end of 6 years your account will have $5,000 + $3,000 = $8,000. Gives you a rough idea of what the actual answer should be, but as you can see it is "rough" because it's $857.81 lower than it should be.
.
I hope this helps you to understand the problem a little better and also to see how to use the formula to solve it. Keep working on this. In real life you absolutely need to understand how to work with your money to your advantage! You might try this problem again only using a 0.1% interest rate that banks are paying today on savings accounts. (Yes, that's right. One-tenth of 1% or a rate of 0.001). See how little your $5,000 will return in 6 years. The answer is that in 6 years you will have $5030.08 in your account, about $3,827 less than you would have at a 10% interest rate for the same period. Be smart. Lack of knowledge can be expensive.
.
Good Luck with this!!!
|
|
|
