Peter deposited RM 1,536 on 15 May 2010 into account that pays 10% compounded quarterly. Find the interest earned on 15 February 2015
P = Po(1+r)^n.
r = 0.10/4 = 0.025 = quarterly % rate.
n = 4*4.75 = 19 compounding periods.
P = 1536(1+0.025)^19 = 2455.53
I = P-Po =
To find the interest earned on 15 February 2015, we need to calculate the amount of money that Peter will have in his account after the 4.75 years (from 15 May 2010 to 15 February 2015) and then subtract the initial deposit.
We can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years the money is invested for
Given:
P = RM 1,536
r = 10% = 0.10 (in decimal form)
n = 4 (compounded quarterly)
t = 4.75 years
Substituting the values into the formula:
A = 1,536(1 + 0.10/4)^(4*4.75)
Simplifying the formula:
A = 1,536(1 + 0.025)^(19)
A = 1,536(1.025)^(19)
Calculating the value of (1.025)^(19):
(1.025)^(19) = 1.542408059
Now, substitute this value back into the formula:
A = 1,536 * 1.542408059
A ≈ 2,368.29
So, Peter will have approximately RM 2,368.29 in his account on 15 February 2015.
To find the interest earned, we need to subtract the initial deposit:
Interest = A - P
Interest = 2,368.29 - 1,536
Interest ≈ RM 832.29
Therefore, the interest earned on 15 February 2015 is approximately RM 832.29.
To find the interest earned, we need to use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = the final amount (principal + interest)
P = the principal (initial deposit)
r = annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
First, let's calculate the principal and the number of years:
Principal (P) = RM 1536
To calculate the number of years (t), we need to find the difference between the given date (15 February 2015) and the date of the initial deposit (15 May 2010).
Years (t) = (2015 - 2010) = 5 years
Next, let's determine the interest rate (r) and the compounding frequency (n):
The interest rate is given as 10% compounded quarterly, which means it is compounded four times per year. So, the interest rate (r) is 10% or 0.10, and the compounding frequency (n) is 4.
Now we can calculate the final amount (A) using the formula for compound interest:
A = P (1 + r/n)^(nt)
A = RM 1536 (1 + 0.10/4)^(4*5)
A = RM 1536 (1 + 0.025)^(20)
A = RM 1536 (1.025)^(20)
A ≈ RM 2271.39
To find the interest earned, we subtract the principal from the final amount:
Interest earned = A - P
Interest earned = RM 2271.39 - RM 1536
Interest earned ≈ RM 735.39
Therefore, the interest earned on 15 February 2015 is approximately RM 735.39.