Your aunt has gifted you a growing perpetuity. The first payment will occur in a year and will be $3,739. Each year after that, on the anniversary of the last payment, you will receive a payment that is 3% larger than the last payment. This pattern of payments will go on forever. If the interest rate is 10% per year, the value of the bequest today is closest to? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)

The value of a perpetuity can be calculated using the formula: $$\[ V = \frac{C}{r}, \]$$ where: - V is the value of the perpetuity, - C is the annual payment (also known as the coupon or dividend payment), - r is the discount rate (interest rate). In this case, the annual payment starts at $3,739 and increases by 3% each year. The interest rate is 10% per year. Let's calculate the value of the perpetuity: First Year Payment: $$\( C_1 = \$3,739 \)$$ Second Year Payment: $$\( C_2 = C_1 \times 1.03 = \$3,739 \times 1.03 \)$$ Third Year Payment: $$\( C_3 = C_2 \times 1.03 = C_1 \times 1.03^2 \)$$ and so on... The sum of all these payments can be expressed as an infinite geometric series: $$\[ S = C_1 + C_2 + C_3 + \ldots = C_1 + C_1 \times 1.03 + C_1 \times 1.03^2 + \ldots. \]$$ The sum of an infinite geometric series is given by: $$\[ S = \frac{C_1}{1 - r}, \]$$ where r is the common ratio (in this case, 1.03). So, the value of the perpetuity V is: $$\[ V = \frac{C_1}{r} = \frac{\$3,739}{0.10} = \$37,390. \]$$ Rounded to two decimal places, the value of the perpetuity is closest to $37,390.00.