A person places $52300 in an investment account earning an annual rate of 7.5%, compounded continuously. Using the formula V=Pe^(rt), where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years. Answer:

Question

A person places  $52300 in an investment account earning an annual rate of  7.5%, compounded continuously. Using the formula  V=Pe^(rt), where  V is the value of the account in t years,  P is the principal initially invested,  e is the base of a natural logarithm, and  r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years. Answer:

Bytelearn · Accepted Answer

Identify Values: Identify the given values from the problem. Principal (P) = $52,300 Rate of interest (r) = 7.5% or 0.075 (as a decimal) Time (t) = 7 years We will use the formula for continuous compounding: V = Pe^(rt)Convert Percentage to Decimal: Convert the percentage rate to a decimal. 7.5% as a decimal is 0.075.Substitute Values: Substitute the given values into the formula. V = 52300 * e^(0.075 * 7)Calculate Exponent: Calculate the exponent part of the formula. 0.075 * 7 = 0.525Calculate e Value: Calculate e raised to the power of the result from Step 4. e^0.525 (Use a calculator for this step)Multiply Principal: Multiply the principal by the result from Step 5. V = 52300 * e^0.525 (Use a calculator to find the value of e^0.525 and then multiply by 52300)Round Final Result: Round the final result to the nearest cent. (Use a calculator to complete the calculation and round to the nearest cent)

Full solution

More problems from Compound interest

Related topics