Question

In: Finance

You have found a mutual fund that you would like to invest in that will earn...

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
		$10,000
		$12,578
		$1,628

Expert Solution

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

jeff jeffy answered 11 months ago

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