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Suppose you have $5400 deposited at 3.6% compounded semiannually. About long will it take your balance to increase to $7100? Round value to one decimal place. years

Suppose you have $5400 deposited at 3.6% compounded semiannually. About long will it take your balance to increase to $7100? Round value to one decimal place. years

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose you have $5400 deposited at 3.6% compounded semiannually. About how long will it take your balance to increase to $7100? Round value to one decimal place. [Input Box] years
Transcribed Image Text:Suppose you have $5400 deposited at 3.6% compounded semiannually. About how long will it take your balance to increase to $7100? Round value to one decimal place. [Input Box] years
Expert Solution
Step 1: Introduction

Given information:

  • Initial deposit (principal), P space equals space $ 5400.
  • Annual interest rate, r space equals space 3.6 percent sign
  • Compounding frequency, n space equals space 2 (semi-annually).
  • Desired balance, A space equals space $ 7100.

To find:

The time it will take for the balance to increase to $ 7100.

Concept used:

We can use the compound interest formula to find the time it takes for the initial deposit to grow to the desired balance when interest is compounded semi-annually.

Formula used:

The formula for compound interest is given by:

Where:

  • A space equals the final balance
  • P space equals the initial principal
  • r space equals annual interest rate (in decimal form)
  • n space equals the number of times interest is compounded per year
  • t space equals the time (in years)
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