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Joe is taking out a loan for $1,500 with an annual compound interest rate of 15% for 3 years. Joe will not make any additional deposits or withdrawals. What will be the total balance paid at the end of 3 years?

Joe is taking out a loan for $1,500 \$ 1,500 with an annual compound interest rate of 15% 15 \% for 33 years. Joe will not make any additional deposits or withdrawals. What will be the total balance paid at the end of 33 years?

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Q. Joe is taking out a loan for $1,500 \$ 1,500 with an annual compound interest rate of 15% 15 \% for 33 years. Joe will not make any additional deposits or withdrawals. What will be the total balance paid at the end of 33 years?
  1. Identify Variables: Identify the variables for the compound interest formula.\newlinePrincipal amount PP = $1,500\$1,500\newlineAnnual interest rate rr = 15%15\% or 0.150.15 (as a decimal)\newlineNumber of years tt = 33\newlineCompound frequency nn = 11 (since no specific compounding frequency is mentioned, we assume it is compounded annually)
  2. Use Formula: Use the compound interest formula to calculate the total balance at the end of 33 years.\newlineThe compound interest formula is A=P(1+r/n)(nt)A = P(1 + r/n)^{(nt)}, where AA is the amount of money accumulated after nn years, including interest.\newlineSubstitute the given values into the formula:\newlineA=1500(1+0.15/1)(1∗3)A = 1500(1 + 0.15/1)^{(1*3)}
  3. Calculate Total Balance: Calculate the total balance using the formula.\newlineA=1500(1+0.15)3A = 1500(1 + 0.15)^{3}\newlineA=1500(1.15)3A = 1500(1.15)^{3}\newlineA=1500×1.153A = 1500 \times 1.15^3\newlineA=1500×1.520875A = 1500 \times 1.520875\newlineA=2281.3125A = 2281.3125
  4. Check Calculation: Check the calculation for any mathematical errors.\newlineRe-evaluate the exponent:\newline1.153=1.5208751.15^3 = 1.520875 (correct)\newlineMultiply by the principal amount:\newline1500×1.520875=2281.31251500 \times 1.520875 = 2281.3125 (correct)

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