Question

"You put $3,200 in an account for 36 months. the account accumulates to

$6,527.64. what is the interest per monthly period ?"

Answer 1

To calculate the monthly interest rate from a $3,200 investment that grows to $6,527.64 in 36 months, use the formula A = P(1 + r)^n and solve for r. The formula rearranges to r = (A/P)^(1/n) - 1. Plugging the values into this equation will yield the monthly interest rate.

Step-by-step explanation:

The question asks to calculate the interest per monthly period on a bank account that was initially invested with $3,200 and grew to $6,527.64 over 36 months. To solve this, we first need to understand the concept of compound interest, which is the interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan.

Let's denote the initial principal by P, the final amount by A, the interest rate per period by r, and the number of periods by n. The formula for compound interest is:

A = P(1 + r)^n

In this question:

• P = $3,200
• A = $6,527.64
• n = 36 (since it's over 36 months)

To find the monthly interest rate (r), we rearrange the formula to solve for r:

r = (A/P)^(1/n) - 1

Plugging in the values, we get:

r = ($6,527.64 / $3,200)^(1/36) - 1

After calculating the value, we'll get the interest rate per monthly period. It's important to note that in situations like this, the value is expressed as a decimal, not a percentage. To express it as a percentage, you would need to multiply the decimal by 100.

Answer 2

To determine the interest per monthly period, the formula for compound interest, A = P(1 + r/n)^nt, is used. However, without the exact interest rate, the accurate calculation cannot be completed. The monthly interest rate can be found by rearranging the formula to solve for the annual rate and then dividing by 12.

Step-by-step explanation:

The question asks to calculate the interest per monthly period for an account where $3,200 accumulates to $6,527.64 in 36 months. To find the monthly interest rate, you would typically use the formula for compound interest, which is A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for, in years.

In this case, however, since we don't know the interest rate and we are looking for the monthly interest rate, we would need to re-arrange the formula to solve for r, and then convert that annual rate into a monthly rate by dividing by 12. Since we have the time in months, we can simplify by considering n as 1 for monthly compounding. We would then calculate r in the formula P(1 + r)t = A, and solve for r using logarithms. The calculation steps would involve finding the compound interest, and then deducing the monthly interest rate from that.

Note: The complete calculation was not performed as the exact interest rate was not provided in the question, hence an accurate and complete solution cannot be given.