Question

If $7500 is invested at 14.3% compounded continuously, the future value s at any time t (in years) is given by the following formula. (round your answers to two decimal places.) s = 7500e0.143t (a) what is the amount after 18 months? s = $ 9,294.32 (b) how long before the investment doubles? t = yr

Answer 1

The amount after 18 months of continuous compounding at 14.3% is approximately $9,294.32. For the investment to double, it would take roughly 4.85 years, highlighting the significant effects of compound interest over time.

Step-by-step explanation:

To address part (a), we calculate the future value (s) after 18 months (1.5 years) using the given formula for continuous compounding, which is s = 7500e0.143t. Substituting 1.5 for t gives us:

s = 7500 e(0.143 × 1.5)

s = 7500 e0.2145

s ≈ 9294.32

For part (b), we want to find the time (t) it takes for the investment to double its original amount. We solve for t in the equation 2 × 7500 = 7500e0.143t:

2 = e0.143t

⌊ ln(2) / 0.143 ⌋ ≈ t

t ≈ ⌊ ln(2) / 0.143 ⌋

t ≈ 4.85 years

This process demonstrates the power of compound interest and its impact on investments over time.