Math Problem Statement

Future value calculation   Without referring to the preprogrammed function on your financial

calculator​,

use the basic formula for future value along with the given interest​ rate,

r​,

and the number of​ periods,

n​,

to calculate the future value of​ $1 in the case shown in the following table. Interest​ rate,** r**

Number of​ periods,** n**

77​%

20 The future value of​ $1 is

​$enter your response here.

​(Round to three decimal​ places.)

Solution

The future value FVFV of $1 can be calculated using the formula:

FV=P(1+r)nFV = P(1 + r)^n

Where:

  • PP is the initial amount (in this case, P=1P = 1).
  • rr is the interest rate per period (expressed as a decimal).
  • nn is the number of periods.

Given:

  • r=77%r = 77\% or r=0.77r = 0.77,
  • n=20n = 20 periods,

We can calculate the future value:

FV=1(1+0.77)20FV = 1(1 + 0.77)^{20}

Let me compute this for you.The future value of $1 at an interest rate of 77% over 20 periods is approximately $91,088.873 (rounded to three decimal places).

Would you like more details or have any questions?

Here are 5 related questions for deeper understanding:

  1. How does the future value change if the interest rate decreases?
  2. What happens to the future value if the number of periods increases?
  3. How does compound interest affect long-term investments?
  4. Can you calculate the future value for different initial amounts?
  5. What is the difference between simple interest and compound interest?

Tip: A higher interest rate or more periods significantly increases the future value due to compound interest effects.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

Future Value (FV) formula: FV = P(1 + r)^n

Theorems

Compound Interest Theorem

Suitable Grade Level

Grades 10-12