Question

Determine the interest rate if a $2000 investment is compounded quarterly for 5 years, and the current amount in the bank is $2564.07.

a) 3.0%

b) 4.5%

c) 5.0%

d) 6.2%

Answer 1

The interest rate is approximately 5.0%.

Step-by-step explanation:

To determine the interest rate, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A = current amount in the bank ($2564.07)
• P = principal amount ($2000)
• r = interest rate (unknown)
• n = compounding frequency per year (quarterly)
• t = number of years (5)

Plugging in the values, we have:

2564.07 = 2000(1 + r/4)^(4*5)

Rearranging the equation and isolating r, we get:

r = 4[(2564.07/2000)^(1/20) - 1]

Simplifying the expression, the interest rate is approximately 5.0%.