Question

Jose hopes to earn $1400 in interest in 3.4 years times from $56,000

Answer 1

Step-by-step explanation

To solve this problem, we will use the formula for compound interest:

`r=k\cdot(((P_N)/(P_0))^(1/(NK))-1).`

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:

`r=4\cdot(((57400)/(56000))^(1/(3.4\cdot4))-1)\cong0.00727=0.73\%.`Answer

The annual interest must be 0.73%.