A bank offers two interest account plans. Plan A gives you 6% interest compound 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?
Plan A $524.95
Plan B $524.95
Plan B $1,040.00••
Plan A $1,040.00
Correct me
you are correct.
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plan A1,040.00
Sorry for the confusion, you are correct. Plan A would earn you $524.95 in interest after 4 years and Plan B would earn you $1,040.00. Therefore, Plan B earns you the most interest (in dollars) after 4 years.
Well, well, well, looks like we've got ourselves a little interest dilemma! Let's calculate the numbers and see who takes the crown.
In Plan A, we've got compound interest at 6% annually. So, after 4 years, the formula for compound interest can be used: A = P(1+r/n)^(n*t), where A is the total amount, P is the principal (initial investment), r is the interest rate, n is the number of times interest is compounded per year (annually in this case), and t is the number of years.
Applying the formula for Plan A: A = 2000(1+0.06/1)^(1*4) = $2,524.95.
Now, onto Plan B, our simple interest friend. With 13% simple interest, we can use the formula: I = P*r*t, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
Applying the formula for Plan B: I = 2000*0.13*4 = $1,040.00.
So, my dear friend, Plan B earns you the most interest after 4 years, with a whopping $1,040.00! Looks like we've found the winner in this interest battle.
To determine which account will earn you the most interest after 4 years, we need to calculate the interest earned using both Plan A and Plan B.
In Plan A, the interest is compounded annually, which means that the interest earned each year will be added to the initial investment. The formula to calculate the future value with compound interest is:
FV = P(1 + r/n)^(n*t)
Where:
FV = Future Value
P = Initial investment
r = Annual interest rate
n = Number of times the interest is compounded per year
t = Number of years
Using the given values:
P = $2,000
r = 6% or 0.06 (as a decimal)
n = 1 (since interest is compounded annually)
t = 4 years
FV(A) = 2000(1 + 0.06/1)^(1*4)
= 2000(1.06)^4
= 2000(1.262476)
= $2524.95
So, according to Plan A, after 4 years, you would have earned $524.95 in interest.
In Plan B, the interest is calculated using simple interest, which means that the interest earned each year is based on the initial investment only. The formula to calculate the future value with simple interest is:
FV = P(1 + r*t)
Where:
FV = Future Value
P = Initial investment
r = Annual interest rate
t = Number of years
Using the given values:
P = $2,000
r = 13% or 0.13 (as a decimal)
t = 4 years
FV(B) = 2000(1 + 0.13*4)
= 2000(1.52)
= $3040
So, according to Plan B, after 4 years, you would have earned $1040 in interest.
Therefore, the correct answer is:
Plan B, $1,040.00