A bank offers two interest account plans. Plan A gives you 6% interest compounded annually. Plan B gives you 13% annual simple interest. You plan to invest 2,000 for the next 4 years. Which account earns you the most interest (in dollars) after 4 years? How much will you have earned?
um that didn't help
thanks helped alot
That didn’t help
Answer beggers and thanks helped out reiny!
To find out which account earns the most interest in dollars after 4 years and how much you will have earned, we need to calculate the interest earned under each account plan.
Let's start with Plan A, which offers 6% interest compounded annually. The formula to calculate the compound interest is:
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
In this case, for Plan A:
P = $2,000
r = 6% or 0.06 (in decimal form)
n = 1 (annually compounded)
t = 4 years
Using the formula, we can calculate the future value (A) for Plan A:
A = $2,000(1 + 0.06/1)^(1*4)
A = $2,000(1 + 0.06)^4
A = $2,000(1.06)^4
A ≈ $2,508.85
Therefore, with Plan A, you will have earned approximately $2,508.85 - $2,000 = $508.85 in interest after 4 years.
Now, let's move on to Plan B, which offers 13% annual simple interest. The formula to calculate the simple interest is:
I = P * r * t
Where:
I = the interest earned
P = the principal investment amount (initial deposit)
r = annual interest rate (in decimal form)
t = number of years
In this case, for Plan B:
P = $2,000
r = 13% or 0.13 (in decimal form)
t = 4 years
Using the formula, we can calculate the interest earned (I) for Plan B:
I = $2,000 * 0.13 * 4
I = $1,040
Therefore, with Plan B, you will have earned $1,040 in interest after 4 years.
Comparing the results, Plan A earned $508.85 in interest, while Plan B earned $1,040 in interest. Therefore, Plan B, with the 13% simple interest, earns you the most interest after 4 years.
Keep in mind that these calculations assume that no additional deposits or withdrawals are made during the 4-year period and that the interest rates remain constant.
Without even doing any calculation, since there is such a large difference in the interest rates, it should be obvious that the simple interest plan should be the better of the two.
check:
at simple interest
I = 2000(.13)(4) = 1040
so amount in your account = 3040
at compound interest:
amount = 2000(1.06)^4 = 2524.95
Unrealistic interest rates, time to get a new textbook