An investment of $2500 accumulates at 6% p.a compounded semi annually for 3 years. At that time, the interest rate is changed to 5% compounded monthly. How much is the investment worth 2 years after the change in interest rate? What is interest gained at the end of the 5 years.

2500 * (1.03^6) = 2985.13

now 2985.13 (1+ .05/12)^24 = 3298.39

3298.39 -2500 = 798.39

tisa received $5200 on a deposit she made five years and eight months ago. The interest rate was is 6.7% p.a. compounded quaterly. How much interest was included in amount he received?

To calculate the worth of the investment 2 years after the change in interest rate, we need to calculate the future value for each period separately and then add them together.

First, let's calculate the future value of the investment for the initial 3 years at a 6% interest rate compounded semi-annually:

Step 1: Convert the annual interest rate to a semi-annual interest rate:
The interest rate of 6% p.a compounded semi-annually becomes:

6% / 2 = 3% interest rate compounded semi-annually

Step 2: Calculate the future value for the initial 3 years:
Using the formula for compound interest:

FV = PV * (1 + r/n)^(n*t)

where FV is the future value, PV is the present value, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

FV = $2,500 * (1 + 0.03/2)^(2*3)
FV = $2,500 * (1.015)^6
FV ≈ $2,807.03

The investment is worth approximately $2,807.03 after 3 years at the initial interest rate.

Next, let's calculate the future value of the investment for the remaining 2 years at a 5% interest rate compounded monthly:

Step 3: Convert the annual interest rate to a monthly interest rate:
The interest rate of 5% p.a compounded monthly becomes:

5% / 12 = 0.4167% interest rate compounded monthly

Step 4: Calculate the future value for the remaining 2 years:
Using the same formula for compound interest:

FV = PV * (1 + r/n)^(n*t)

FV = $2,807.03 * (1 + 0.004167/1)^(1*12*2)
FV ≈ $2,981.68

The investment is worth approximately $2,981.68 after 2 years at the changed interest rate.

To calculate the total interest gained at the end of the 5 years, we subtract the initial principal from the final amount:

Interest gained = Total future value - Initial investment
= $2,981.68 - $2,500
= $481.68

Therefore, the interest gained at the end of the 5 years is approximately $481.68.