Simple Interest: Number of Years

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SUMMARY

The discussion centers on calculating the number of years required for the cumulative value of interest to equal the original investment using the simple interest formula. The correct formula is identified as interest = Prt, where P is the principal amount, r is the interest rate (0.125 for 12.5%), and t is the number of years. A user mistakenly applied the formula V=P(1+rt), leading to incorrect calculations. The correct approach involves solving for t when the interest equals the principal.

PREREQUISITES
  • Understanding of simple interest calculations
  • Familiarity with the formula for simple interest: interest = Prt
  • Basic algebra skills for solving equations
  • Knowledge of percentage conversion (e.g., converting 12.5% to 0.125)
NEXT STEPS
  • Practice solving simple interest problems using the formula interest = Prt
  • Explore the implications of varying interest rates on investment duration
  • Learn how to derive the formula for calculating the time required for interest to equal the principal
  • Investigate real-world applications of simple interest in finance
USEFUL FOR

Students studying finance or mathematics, educators teaching simple interest concepts, and anyone looking to understand investment growth over time.

zak100
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Homework Statement


An investment is made at 12.5% annual simple interest. Find the number of years it will take for the cumulative value of the interest to equal the original investment?

Homework Equations


V=P(1+rt)
Where V= interest on Amount
P = Principal amount
r= interest rate
t= number of years for which amount is invested

The Attempt at a Solution


Simple Interest formula is:

V=P(1+rt) Let p =10 & t=1

V= 10(1+12.5) = 135In just one year the interest obtained is more than the Principal value. Some body please guide me. What I understand is that, I have to find the number of years in which the interest obtained & added (with previous years’ interest becomes equal to the Principal).

Zulfi.
 
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r is 12.5%, which is 0.125, not 12.5.
 
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zak100 said:

Homework Statement


An investment is made at 12.5% annual simple interest. Find the number of years it will take for the cumulative value of the interest to equal the original investment?

Homework Equations


V=P(1+rt)
Where V= interest on Amount
P = Principal amount
r= interest rate
t= number of years for which amount is invested

The Attempt at a Solution


Simple Interest formula is:

V=P(1+rt) Let p =10 & t=1

V= 10(1+12.5) = 135In just one year the interest obtained is more than the Principal value. Some body please guide me. What I understand is that, I have to find the number of years in which the interest obtained & added (with previous years’ interest becomes equal to the Principal).

Zulfi.

Your formula for the interest is wrong: interest = Prt, NOT P(1+rt).
 

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