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 |
||

$10,000 |
||

$12,578 |
||

$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

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