A bank offers 5% compound interest on investments.A men invest $2000.
a)what is his investment worth after three year?
b)find the compound interest.
What is the compounding period ? Yearly? Monthly? Daily?
Remember that Amount in account = Principal(1 + i)^(n)
To calculate the investment worth and compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
a) Investment worth after three years:
To find the investment worth after three years, we need to substitute the given values into the formula. Let's calculate it step by step.
P = $2000 (Principal amount)
r = 5% (Annual interest rate, expressed as 0.05)
n = 1 (Since interest is compounded annually)
t = 3 (Number of years)
A = $2000(1 + 0.05/1)^(1*3)
A = $2000(1 + 0.05)^3
A = $2000(1.05)^3
A ≈ $2000 * 1.157625
A ≈ $2315.25
Therefore, the investment is worth approximately $2315.25 after three years.
b) Compound interest:
To find the compound interest, we can subtract the principal amount (initial investment) from the final amount.
Compound interest = A - P
Compound interest = $2315.25 - $2000
Compound interest ≈ $315.25
So, the compound interest earned on the investment is approximately $315.25.