Explanation
To solve this problem, we will use the formula for compound interest:
[tex]r=k\cdot((\frac{P_N}{P_0})^{1/(NK)}-1).[/tex]
Where:
• Pₙ = principal amount after N years,
,
• P₀ = initial principal amount,
,
• r = interest ratio in decimals,
,
• k = compound periods per year.
From the statement, we know that:
• N = 3.4 years,
• P₀ = $56,000,
• Pₙ = P₀ + interest = $56,000 + $1,400 = $57,400,
,
• r = ?,
,
• k = 4 (the interest is compounded quarterly.
Replacing these values in the formula above, we get:
[tex]r=4\cdot((\frac{57400}{56000})^{1/(3.4\cdot4)}-1)\cong0.00727=0.73\%.[/tex]Answer
The annual interest must be 0.73%.
