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PLEASE USE EXCEL! Part 2 Find the future value of an increasing annuity. Imagine you want to accumulate certain amount, or future value, by making
PLEASE USE EXCEL!
Part
Find the future value of an increasing annuity.
Imagine you want to accumulate certain amount, or future value, by making the same payments for
certain number of periods. How much should your payments be
Strategy for solution:
To develop the general formula let's first figure out the future value of payments of $
The future value of the last payment made at time is just $
The future value of the next to last payment made at time is just $ the accumulated value
of a payment of $ over one period.
The future value of the payment made at time is $ the accumulated value of a payment
of $ over periods.
The future value of the payment made at time is $ the accumulated value of a payment of
$ over periods.
The future value of all payments is the sum
cdots
In order to find a general formula for this sum, we need to review the sum of geometric progression.
A geometric series is always going to look like
cdots for some number
Now, what does this have to do with finance? Let's look at an example.
Let cdots
cdots
cdots
The difference is:
In our example thus we have
The future value when the payment is equal to is:
Questions to answer:
Imagine that you want to invest into an increasing annuity to accumulate a certain amount of money
by the time you graduate. To make it more realistic, think of the set amount of money you can put away
every month.
a Using Excel, calculate how much will you have by the time you graduate from college if you make a set
payment into this annuity every month?
b Using Excel, calculate how much will you have after you make payments?
c Confirm result you received in part b by populating the following table and using the same logic as
was used to develop the formula for future value of increasing annuity.
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