On 16 April 2013, RM 2,000 was invested at 5% compounded semi annually. Find the amount accumulated on 16 October 2016 if the rate was changed to 8% compounded quarterly beginning 16 April 2014.
find out the amount accumulated at 16 Oct: 13 quarters
value= 2000 (1.0125)^13= about 2259
Now, that is compounded 7 quarters...
value=2259(1.020)^7= about 2594
check my thinking and math.
Oh, calculations and investments, my favorite! So, let's break it down.
From 16 April 2013 to 16 April 2014, the investment was compounded semi-annually at a rate of 5%. So, we'll calculate the amount accumulated until April 2014.
The formula to calculate compound interest is: A = P(1 + r/n)^(n*t), where A is the amount, P is the principal, r is the rate, n is the number of times compounded per year, and t is the time in years.
Using the formula, we have:
A = 2000(1 + 0.05/2)^(2*1)
A = 2000(1 + 0.025)^2
A ≈ 2000(1.025)^2
A ≈ 2050.63
So, the amount accumulated until 16 April 2014 is approximately RM 2050.63.
Now, let's calculate the amount accumulated from 16 April 2014 to 16 October 2016. The rate has changed to 8% and it's compounded quarterly.
Using the same formula, we have:
A = 2050.63(1 + 0.08/4)^(4*2.5)
A ≈ 2050.63(1.02)^10
A ≈ 2050.63(1.218996)
A ≈ 2498.01
Therefore, the amount accumulated on 16 October 2016 is approximately RM 2498.01.
Remember, investing can be a bit like juggling. You have to keep track of different rates, dates, and formulas. But in the end, it's all worth it when you see your money grow!
To calculate the amount accumulated on 16 October 2016, we need to calculate the amounts accumulated over different periods of time, each with different interest rates.
Step 1: Calculate the amount accumulated from 16 April 2013 to 16 April 2014 using a 5% interest rate compounded semiannually.
Let's use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount accumulated
P = the principal amount (RM 2,000)
r = annual interest rate (5%)
n = number of times interest is compounded per year (semiannually)
t = time in years (1)
Substituting the values, we get:
A1 = 2000(1 + 0.05/2)^(2*1)
A1 = 2000(1 + 0.025)^(2)
A1 = 2000(1.025)^(2)
A1 = 2000(1.050625)
A1 ≈ RM 2,101.25
Step 2: Calculate the amount accumulated from 16 April 2014 to 16 October 2016 using an 8% interest rate compounded quarterly.
Since the rate changed on 16 April 2014, we need to calculate the time from that date to 16 October 2016. This is approximately 2.5 years.
Using the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount accumulated
P = the principal amount (RM 2,101.25, which is the accumulated amount from Step 1)
r = annual interest rate (8%)
n = number of times interest is compounded per year (quarterly)
t = time in years (2.5)
Substituting the values, we get:
A2 = 2101.25(1 + 0.08/4)^(4*2.5)
A2 = 2101.25(1 + 0.02)^(10)
A2 = 2101.25(1.02)^(10)
A2 ≈ RM 2,873.27
Step 3: Calculate the overall amount accumulated from 16 April 2013 to 16 October 2016.
The overall amount accumulated is the sum of the amounts accumulated in Step 1 and Step 2.
A overall = A1 + A2
A overall = 2,101.25 + 2,873.27
A overall ≈ RM 4,974.52
Therefore, the amount accumulated on 16 October 2016 is approximately RM 4,974.52.
To find the amount accumulated on 16 October 2016, we need to calculate the accumulated value of the two separate periods with different interest rates and compounding frequencies.
First, let's calculate the accumulation from 16 April 2013 to 16 April 2014 at a 5% interest rate compounded semiannually.
The formula to calculate the accumulated value with compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated Value
P = Principal (initial investment)
r = Interest rate (as a decimal)
n = Compounding frequency per year
t = Time in years
For the first period:
P = RM 2,000
r = 5% = 0.05 (as a decimal)
n = 2 (semiannually)
t = 1 (year)
Using the formula, we can calculate the accumulated value at the end of the first period:
A1 = 2000(1 + 0.05/2)^(2*1)
= 2000(1 + 0.025)^2
= 2000(1.025)^2
= 2000(1.050625)
= 2101.25
So, the accumulated value on 16 April 2014 is RM 2,101.25.
Now, let's calculate the accumulation for the second period from 16 April 2014 to 16 October 2016 at an 8% interest rate compounded quarterly.
For the second period:
P = RM 2,101.25 (accumulated value from the first period)
r = 8% = 0.08 (as a decimal)
n = 4 (quarterly)
t = 2.5 years (from 16 April 2014 to 16 October 2016)
Using the formula, we can calculate the accumulated value at the end of the second period:
A2 = 2101.25(1 + 0.08/4)^(4*2.5)
= 2101.25(1 + 0.02)^(10)
= 2101.25(1.02)^10
= 2101.25(1.218994)
= 2560.08
Therefore, the amount accumulated on 16 October 2016 is approximately RM 2,560.08.