Determine the compound interest earned on each investment $920 compounded weekly at 10.4% per annum for 4 years

Identify Variables: Identify the principal amount (P), annual interest rate (r), number of times the interest is compounded per year (n), and the number of years the money is invested or borrowed for (t). P = $920 r = 10.4% per annum = 0.104 (in decimal) n = 52 (since interest is compounded weekly) t = 4 yearsCompound Interest Formula: Use the compound interest formula A = P(1 + r/n)^(nt) to find the total amount (A) after 4 years.Substitute Values: Substitute the values into the formula. A = 920(1 + 0.104/52)^(52*4)Calculate Values: Calculate the values inside the parentheses and the exponent. A = 920(1 + 0.002)^(208) A = 920(1.002)^(208)Calculate Total Amount: Calculate the total amount A using a calculator. A ≈ 920 * (1.002)^208 A ≈ 920 * 1.9994 A ≈ 1839.248Calculate Compound Interest: Calculate the compound interest earned by subtracting the principal amount (P) from the total amount (A). Compound Interest = A - P Compound Interest ≈ 1839.248 - 920 Compound Interest ≈ 919.248

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Determine the compound interest earned on each investment
$920 compounded weekly at 10.4% per annum for 4 years

Determine the compound interest earned on each investment $\newline$ $\$ 920$ compounded weekly at $10.4 \%$ per annum for $4$ years

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Algebra 1

Exponential growth and decay: word problems

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Q. Determine the compound interest earned on each investment

\newline

\$ 920

compounded weekly at

10.4 \%

per annum for

4

years

Identify Variables: Identify the principal amount $P$ , annual interest rate $r$ , number of times the interest is compounded per year $n$ , and the number of years the money is invested or borrowed for $t$ . $P = \$920$ $r = 10.4\%$ per annum $= 0.104$ (in decimal) $n = 52$ (since interest is compounded weekly) $t = 4$ years
Compound Interest Formula: Use the compound interest formula $A = P(1 + r/n)^{(nt)}$ to find the total amount ( $A$ ) after $4$ years.
Substitute Values: Substitute the values into the formula. $\newline$ $A = 920(1 + 0.104/52)^{52\times 4}$
Calculate Values: Calculate the values inside the parentheses and the exponent. $\newline$ $A = 920(1 + 0.002)^{208}$ $\newline$ $A = 920(1.002)^{208}$
Calculate Total Amount: Calculate the total amount $A$ using a calculator. $\newline$ $A \approx 920 \times (1.002)^{208}$ $\newline$ $A \approx 920 \times 1.9994$ $\newline$ $A \approx 1839.248$
Calculate Compound Interest: Calculate the compound interest earned by subtracting the principal amount $P$ from the total amount $A$ . $\newline$ Compound Interest = $A - P$ $\newline$ Compound Interest $\approx 1839.248 - 920$ $\newline$ Compound Interest $\approx 919.248$