Final answer:
To calculate the future value of an investment with continuous compounding, the formula A = Pe^rt is used. After applying this formula with the given rate of 1.95% compounded continuously for 3 years on a $7,000 deposit, the future value is approximately $7,422.72.
Step-by-step explanation:
To solve the mathematical problem of calculating the future value of Lenny's investment, compounded continuously, we'll use the formula for continuous compounding: A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and t is the time in years.
In Lenny's case, he deposits $7,000 into an IRA that earns 1.95% per year compounded continuously. The equation to find the future value after 3 years would be:
A = 7000e0.0195×3
First, convert the percentage to a decimal by dividing by 100: r = 1.95 / 100 = 0.0195. Then we substitute the values into the formula and perform the calculation:
A = 7000e0.0195×3
Using a calculator with an ex function, we get
A ≈ 7000 × 2.718280.0585 ≈ 7000 × 1.060246 ≈ $7422.72
Therefore, the value of Lenny's investment after 3 years would be approximately $7,422.72 when rounded to the nearest cent, as the final step in our calculation.