Rm 200 was saved every month for four years in an account that pays 6% compounded monthly.find the accumulated value if the interest rate was changed to 8% compounded monthly after one year.
To find the accumulated value, we can break down the problem into two parts:
1. Calculating the accumulated value after four years with an interest rate of 6% compounded monthly.
First, we need to find the number of compounding periods over the four years. Since the interest is compounded monthly, we multiply the number of years by 12:
Number of compounding periods = 4 years * 12 months/year = 48 months
The formula to calculate the accumulated value with compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated value
P = Principal amount (monthly savings)
r = Interest rate per period (6% or 0.06 in decimal form)
n = Number of compounding periods per year (12 since it's compounded monthly)
t = Number of years (4 years)
Plugging in the values, we get:
A = 200(1 + 0.06/12)^(12*4)
Calculating this gives us the accumulated value after four years with an interest rate of 6%.
2. Calculating the accumulated value for the remaining three years with an interest rate of 8% compounded monthly.
After the first year, the interest rate changes to 8% compounded monthly. We need to find the accumulated value for the remaining three years.
Again, we use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
P = Accumulated value from the previous step (after four years at 6% interest rate)
r = New interest rate per period (8% or 0.08 in decimal form)
n = Number of compounding periods per year (12 since it's compounded monthly)
t = Number of years (3 years)
Plugging in the values, we get:
A = Accumulated value from step 1 * (1 + 0.08/12)^(12*3)
Calculating this gives us the accumulated value after three additional years with an interest rate of 8%.
To find the final accumulated value, we add the accumulated value from step 1 (after four years at 6% interest rate) and the accumulated value from step 2 (after three years at 8% interest rate).