Determine the term of a $46000 investment with an interest rate of 3.9%, compounded monthly, if the future value is $100000. Round your answer to the nearest year.
- I know I use the rule of 72 but what do you do after that?
P = Po(1+r)^n
Use same procedure as your 2-16-14, 4:08
AM post.
Po = $46,000
P = $100,000
To determine the term of a compound interest investment using the rule of 72, you can divide 72 by the interest rate to approximate the number of years it will take for the investment to double. However, in this case, we want to find a specific future value of $100,000.
To calculate the term, you can use the formula for compound interest:
Future Value = Present Value x (1 + Interest Rate / Number of Compounding Periods)^(Number of Compounding Periods x Number of Years)
In this case:
Future Value = $100,000
Present Value = $46,000
Interest Rate = 3.9% (or 0.039 as a decimal)
Number of Compounding Periods = 12 (monthly compounding)
We have all the information we need except for the number of years, which is what we want to find.
Step 1: Divide the interest rate by the number of compounding periods:
Interest Rate / Number of Compounding Periods = 0.039 / 12 = 0.00325
Step 2: Rearrange the formula to solve for the number of years:
(Number of Compounding Periods x Number of Years) = log (Future Value / Present Value) / log(1 + Interest Rate / Number of Compounding Periods)
Number of Years = log (Future Value / Present Value) / (Number of Compounding Periods x log(1 + Interest Rate / Number of Compounding Periods))
Step 3: Substitute the values into the formula:
Number of Years = log ($100,000 / $46,000) / (12 x log(1 + 0.00325))
Step 4: Calculate the result:
Number of Years = log (2.1739) / (12 x log(1.00325))
Number of Years = 0.3379 / (12 x 0.0004001)
Number of Years ≈ 0.2815 / 0.00480012
Number of Years ≈ 58.6591
Rounding the answer to the nearest year, the term of the investment would be approximately 59 years.