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How much do you need to invest today at an interest rate of 7% in order to have your investment...

Question:

How much do you need to invest today at an interest rate of 7% in order to have your investment grow to $6,000 in 5 years?

Annuity:

An annuity is an investment opportunity that provides periodic payments of amounts of equal value for a defined period. The payments can be made at the beginning or end of each period called annuity due or ordinary annuity.

Answer and Explanation: 1


The amount that should be invested today is $4,278.

To determine the present value of a single cash flow, we use the formula given below:

{eq}PV=P\times \dfrac{1}{(1+r)^{n}}\\ {/eq}

where

{eq}PV = \text{Present Value of a single payment}\\ P = \text{Amount of payment}\\ r = \text{interest rate}\\ n = \text{number of time periods}\\ {/eq}

On substituting the values:

{eq}PV=$6,000*\frac{1}{(1+0.07)^{5}}\\ PV=$6,000*0.7129862\\ PV=\,$4,278 {/eq}


Learn more about this topic:

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How to Calculate the Present Value of an Annuity

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Chapter 8 / Lesson 3
4.9K

Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.


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