Martina made deposits of $2,000 at the beginning of each year for four years. The rate she earn is 5% annually. What's the value of Marina's account in four years?
a. $8,260.00
b. $11,051.00
c. $9,051.20
d. $8,260.20
My answer is D.
To find the value of Martina's account in four years, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value
P = Payment amount
r = Annual interest rate
n = Number of periods
In this case, Martina deposited $2,000 at the beginning of each year, so P = $2,000. The interest rate is 5% annually, so r = 0.05. The deposits were made for four years, so n = 4.
Plugging these values into the formula:
FV = 2,000 * [(1 + 0.05)^4 - 1] / 0.05
Calculating the expression inside the brackets:
(1 + 0.05)^4 = 1.05^4 = 1.21550625
Substituting this value back into the formula:
FV = 2,000 * (1.21550625 - 1) / 0.05
= 2,000 * 0.21550625 / 0.05
= 8,621.25
Therefore, the value of Martina's account in four years is $8,621.25. Since none of the given answer choices match exactly, the closest option is D. $8,260.20.
To calculate the value of Martina's account after four years, we can use the formula for the future value of an ordinary annuity:
Future Value = P × [(1 + r)^n - 1] / r
Where:
P = annual deposit
r = interest rate per period
n = number of periods
In this case, Martina makes a deposit of $2,000 at the beginning of each year for four years, so P = $2,000, r = 5% (or 0.05 as a decimal), and n = 4.
Plugging these values into the formula:
Future Value = $2,000 × [(1 + 0.05)^4 - 1] / 0.05
Calculating the values within the brackets:
Future Value = $2,000 × [1.05^4 - 1] / 0.05
= $2,000 × [1.21550625 - 1] / 0.05
= $2,000 × [0.21550625] / 0.05
= $2,000 × 4.310125
= $8,620.25
So, the correct answer is not option D. The correct answer is $8,620.25, which is not among the given choices. Therefore, none of the provided options is correct.
r = 0.05
2,000 [(1+r)^n - 1] / r ]
=2,000 [ (1.05^4) - 1] / 0.05
= 11051.26