Calculate the amount and the compound interest: b) on 34,000 for 2 years at the rate of 4.5% p.a. compounded annually.
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Calculate the amount and the compound interest: b) on 34,000 for 2 years at the rate of 4.5% p.a. compounded annually.
Step-by-step explanation:
To calculate the compound interest on an amount, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future amount (including principal and interest)
P = the principal amount (the initial amount you start with)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In your case, you have:
P = $34,000
r = 4.5% per annum, which is 0.045 as a decimal
n = 1 (compounded annually)
t = 2 years
Now, plug these values into the formula:
A = 34,000(1 + 0.045/1)^(1*2)
A = 34,000(1 + 0.045)^2
A = 34,000(1.045)^2
A = 34,000(1.092025)
A ≈ $37,127.85
So, the future amount (including principal and interest) after 2 years is approximately $37,127.85.
To find the compound interest, subtract the principal (initial amount) from the future amount:
Compound Interest = A - P
Compound Interest = $37,127.85 - $34,000
Compound Interest ≈ $3,127.85
The compound interest on $34,000 for 2 years at a rate of 4.5% per annum, compounded annually, is approximately $3,127.85.