6. Which is the better investment?
a) $1200 at 9 percent simple interest for 3 years.
b) $1200 at 8 percent compound interest for 3 years.
To determine which investment is better, we need to calculate the value of both investments after 3 years.
For investment a):
Simple interest formula: I = P * r * t
where I is the interest earned, P is the principal amount, r is the interest rate, and t is the time period.
I = 1200 * 0.09 * 3
I = $324
The value of investment a) after 3 years will be the principal amount plus the interest earned:
Value = 1200 + 324
Value = $1524
For investment b):
Compound interest formula: A = P * (1 + r)^t
where A is the final amount, P is the principal amount, r is the interest rate, and t is the time period.
A = 1200 * (1 + 0.08)^3
A = 1200 * 1.08^3
A = 1200 * 1.2597
A = $1511.64
The value of investment b) after 3 years will be $1511.64.
Comparing the values of both investments, we can see that investment a) is the better choice as it has a higher value ($1524) compared to investment b) ($1511.64).
To determine which investment is better, we need to compare the final amounts obtained from each investment option.
a) $1200 at 9 percent simple interest for 3 years:
To calculate the simple interest, we use the formula: Simple Interest = Principal x Interest Rate x Time.
Simple Interest = $1200 x 0.09 x 3 = $324
So, the final amount after 3 years would be $1200 + $324 = $1524.
b) $1200 at 8 percent compound interest for 3 years:
To calculate the compound interest, we use the formula: Compound Interest = Principal x (1 + Interest Rate)^Time - Principal.
Compound Interest = $1200 x (1 + 0.08)^3 - $1200.
Compound Interest = $1200 x (1.08)^3 - $1200.
Compound Interest = $1200 x (1.259712) - $1200.
Compound Interest = $1511.65 - $1200.
So, the final amount after 3 years would be $1511.65.
Comparing the final amounts, the investment option b) seems to be better as it provides a higher final amount of $1511.65 compared to option a) which gives a final amount of $1524.