In: Finance
You have found a mutual fund that you would like to invest in that will earn 5% annually. If you invest $1000 each year for the next 10 years, how much will you have at the end of those 10 years, approximately?
$18,753 |
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$10,000 |
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$12,578 |
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$1,628 |
Solution:
The formula for calculating the Future value of periodic investments at the end of n years is
= P * [ [ ( 1 + r ) n- 1 ] / r ]
Where P = Periodic Deposit i.e., Fixed amount of Annual deposit
r = rate of interest earned annually ; n = no. of years
A per the information given in the question we have
P = $ 1,000 ; r = 5 % = 0.05 ; n = 10
Applying the above values in the formula we have:
= $ 1000 * [ [ ( 1 + 0.05 ) 10 - 1 ] / 0.05 ]
= $ 1000 * [ [ ( 1.05 ) 10 - 1 ] / 0.05 ]
= $ 1000 * [ [ 1.6289 – 1 ] / 0.05 ]
= $ 1000 * [ 0.6289 / 0.05 ]
= $ 1000 * 12.5780
= $ 12,578
Thus the Solution is Option 3. $ 12,578
Thus if an investment of $1,000 a year is made for a period of 10 years in a mutual fund that earns 5 % annually, the value at the end of 10 years = $ 12,578
Note: The value of ( 1.05 ) 10 is calculated using the Excel formula =POWER(Number,Power)
=POWER(1.05,10)= 1.6289