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What annual investment is required at 8% per year compounded annually to accumulate to $100,000...

Question:

What annual investment is required at 8% per year compounded annually to accumulate to $100,000 at the end of 20 years? (a) $1,800 (b) $2,100 (c) $2,185 (d) $5,200

Annuity:

In the context of Finance, an annuity is a streak of periodic investments or payments made for a given investment horizon. The mechanism of annuity is generally resorted to when one has to accumulate significant retirement fund by making relatively small and regular annual investments.

Answer and Explanation: 1

The calculated value of the annual investment to be made every year for 20 years is option (c) $2,185.

The value of the annual investment amount is given by:

  • {eq}P = F * \dfrac{i}{(1 + i)^ {n} - 1} {/eq}

where;

F = future value of the annuity = $100,000

P = annual investment amount

i = interest rate = 8% (or 0.08)

n = number of years = 20 years

{eq}P = 100,000 * \dfrac{0.08}{(1 + 0.08)^ {20} - 1} {/eq}

{eq}P = $2,185.22 {/eq}


Learn more about this topic:

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How to Find the Value of an Annuity

from

Chapter 21 / Lesson 15

An annuity is a type of savings account that pays back the investor in the future. Learn the formula used to calculate an annuity's value, and understand the importance of labeling specific numbers to calculate an output over time.


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