10.On 16 April 1990, $5000 was invested at 6% compounded semi annually.Find the amount accumulated on 16 October 1993 if the rate was charged to 8% compounded quarterly beginning 16 april 1992.
semi annualy compounding= (2 times in years)
quarterly compounding= (4 times in a year)
how to solve this problem ?i cant understand
Major Hint:
Did you notice that from 16 April to 16 Oct is 6 months?
So your time can be very easily expressed in half-years, and quarter-years.
From all the knowledge you have gained by having received many answers for similar questions to the above, you should now be able to take it from there.
Let me know what you got, and how you did it.
ESCUSE ME,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,WHO WROTE TTTHHHIS HHAAACCCKKKEEERRRSS
To solve this problem, we can break it down into two parts:
1. Calculate the amount accumulated from April 16, 1990, to April 16, 1992, using semi-annual compounding.
2. Calculate the amount accumulated from April 16, 1992, to October 16, 1993, using quarterly compounding.
Part 1: From April 16, 1990, to April 16, 1992
First, let's calculate the number of compounding periods in this period. We have 2 years, and since compounding happens semi-annually (2 times per year), we have a total of 4 compounding periods.
To calculate the amount accumulated, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount accumulated
P = the principal (initial investment)
r = interest rate per period
n = number of compounding periods per year
t = number of years
In this case, the principal (P) is $5000, the interest rate per period (r) is 6% or 0.06, the number of compounding periods per year (n) is 2, and the number of years (t) is 2.
Plugging these values into the formula, we get:
A1 = $5000(1 + 0.06/2)^(2*4)
A1 ≈ $5000(1 + 0.03)^8
A1 ≈ $5000(1.03)^8
A1 ≈ $5000 * 1.2653
A1 ≈ $6326.50
Therefore, the amount accumulated from April 16, 1990, to April 16, 1992, is approximately $6326.50.
Part 2: From April 16, 1992, to October 16, 1993
Next, let's calculate the number of compounding periods in this period. We have 1 year and 6 months, which is equivalent to 1.5 years. Since compounding happens quarterly (4 times per year), we have a total of 6 compounding periods.
Using the same formula as before:
A = P(1 + r/n)^(nt)
The principal (P) remains the same at $6326.50, the interest rate per period (r) is now 8% or 0.08, the number of compounding periods per year (n) is 4, and the number of years (t) is 1.5.
Plugging these values into the formula, we get:
A2 = $6326.50(1 + 0.08/4)^(4*1.5)
A2 ≈ $6326.50(1 + 0.02)^6
A2 ≈ $6326.50(1.02)^6
A2 ≈ $6326.50 * 1.1255
A2 ≈ $7118.34
Therefore, the amount accumulated from April 16, 1992, to October 16, 1993, is approximately $7118.34.
So, the total amount accumulated on October 16, 1993, is the sum of the amounts accumulated in part 1 and part 2:
Total amount accumulated = $6326.50 + $7118.34
Total amount accumulated ≈ $13444.84
Therefore, the amount accumulated on October 16, 1993, is approximately $13,444.84.