Q. Find the value. $3933 invested for 4 years at 5% compounded quarterly
Identify Formula: Identify the formula for compound interest: A=P(1+nr)(nt). Here, A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (decimal). n is the number of times that interest is compounded per year. t is the time the money is invested for in years.
Plug in Values: Plug in the given values into the formula: P=$3933, r=5% or 0.05, n=4 (since interest is compounded quarterly), and t=4 years.
Convert Interest Rate: Convert the percentage interest rate to a decimal: r=5%=0.05.
Calculate Compound Interest: Calculate the compound interest using the formula: A=3933(1+40.05)4×4.
Calculate Values Inside: Calculate the values inside the parentheses and the exponent: A=3933(1+0.0125)16.
Add Values Inside: Add the values inside the parentheses: A=3933(1.0125)16.
Calculate Exponent: Calculate the exponent part: (1.0125)16.
Find Exponent Result: Use a calculator to find (1.0125)16=1.219006942.
Multiply Principal Amount: Multiply the principal amount by the result from the exponent calculation: A=3933×1.219006942.
Find Final Amount: Use a calculator to find the final amount: A=3933×1.219006942=4795.83.
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