Question

Continuously Compounded Interest If a principal of P dollars is deposited in an account paying an annual rate of inter-est R (expressed in decimal form), compounded continuously, then after tyears the account will contain A dollars, where Use the compound interest formula to approximate the final value of each amount . $1500 at 0.75% compounded continuously for 8 years - If college tuition is currently $8000 per year, in lating at 6% per year, what will be the cost of tuition in 10 years? - Determine the best investment: compounding continuously at 6.0% or compound-ing annually at 6.3%

Answer 1

Continuously compounded interest is calculated using the formula A = Pe^(Rt). The formula is applied to the specific scenarios provided to find the future value of the investment or tuition costs, considering the different types of compounding interest rates.

Step-by-step explanation:

To calculate the amount in an account after a certain period with continuously compounded interest, we use the formula A = PeRt, where P is the principal amount, R is the annual interest rate (in decimal form), t is time in years, and e is the base of the natural logarithm (approximately 2.71828).

For the first scenario, with $1500 at 0.75% compounded continuously for 8 years, we would calculate:

A = 1500e(0.0075×8)

For the second scenario, if college tuition currently costs $8000 per year and increases at 6% per year, to find the cost after 10 years, we assume continuous compounding as well:

A = 8000e(0.06×10)

For the third scenario, to determine the best investment between compounding continuously at 6.0% or compounding annually at 6.3%, we would compare:

Continuous compounding after one year: A = P e(0.06×1)

Annual compounding after one year: A = P (1 + 0.063)1

We then assess which final amount is greater to determine the better investment strategy.