Final answer:
a) The value of Kyle's investment after 6 years will be approximately $2,267.47. b) It will take approximately 8.46 years for Kyle's investment to grow to $3,000. c) The interest rate needed to triple Kyle's investment in 15 years is approximately 8.46%.
Step-by-step explanation:
a) To find the value of Kyle's investment after 6 years, we can use the formula A = P*e^(rt), where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years. In this case, P = $1,500, r = 8.25% = 0.0825, and t = 6. Plugging these values into the formula, we get A = 1500*e^(0.0825*6) ≈ $2,267.47.
b) To find how long it will take for Kyle's investment to grow to $3,000, we can use the formula t = (ln(A/P))/(r), where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years. Plugging in the values A = $3,000, P = $1,500, and r = 8.25%, we get t = (ln(3000/1500))/(0.0825) ≈ 8.46 years.
c) To find the interest rate needed to triple Kyle's investment in 15 years, we can use the formula r = (ln(A/P))/(t), where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years. Plugging in the values A = 3*1500 = $4,500, P = $1,500, and t = 15, we get r = (ln(4500/1500))/(15) ≈ 8.46%.