You deposit $1000 in an account at the Lifelong Trust Savings and Loan that pays 7% interest compounded quarterly. By how much will your deposit have grown after 4 years?
You invest $10,000 in Rapid Growth Funds, which appreciate by 1% per year, with yields reinvested quarterly. By how much will your investment have grown after 6 years?
To calculate the growth of the deposit after 4 years, we can use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A is the final amount (the deposit after 4 years)
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the time in years
Given:
P = $1000
r = 7% = 0.07
n = 4 (quarterly compounding)
t = 4 years
Plugging in these values into the compound interest formula, we get:
A = 1000(1 + 0.07/4)^(4*4)
First, let's simplify the value inside the parentheses:
1 + 0.07/4 = 1 + 0.0175 = 1.0175
Next, let's calculate the exponent:
4 * 4 = 16
Now, we can calculate the final amount:
A = 1000(1.0175)^16
Using a calculator, the final amount works out to be approximately $1360.71.
Therefore, your deposit will have grown to approximately $1360.71 after 4 years at an annual interest rate of 7% compounded quarterly.
To calculate the growth of your deposit after 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount (the deposit after 4 years)
- P is the principal amount (the initial deposit)
- r is the annual interest rate (as a decimal)
- n is the number of times the interest is compounded per year
- t is the number of years
In this case, you deposited $1000, the interest rate is 7%, which is equivalent to 0.07 as a decimal. The interest is compounded quarterly, so n is 4. The time we need to calculate for is 4 years:
A = 1000(1 + 0.07/4)^(4*4)
Now, let's calculate it step by step:
First, let's calculate (1 + r/n):
(1 + 0.07/4) = 1.0175
Now, let's calculate (4*4):
4*4 = 16
Finally, substitute the values into the formula:
A = 1000(1.0175)^16
Using a calculator or a computer, evaluate the expression:
A ≈ $1311.44
Therefore, your deposit will have grown to approximately $1311.44 after 4 years at an annual interest rate of 7%, compounded quarterly.
for the deposit, use thsi as your equation:
1000(1+.07)^4
for the investment in RGF use this as your equation:
10000(1+.01)^6
Just plug them into a calulator to solve.