The annual interest rate needed to reach the given amount in five years is 4.47%.
Hence, option B) is the correct answer.
What is the annual interest rate needed?
Compound interest is expressed as;
A = P( 1 + r/n )^(nt)
Making rate r the subject of the formula;
r = n[ (A/P)^(1/nt) - 1 ]
Given that;
- Principal P $2000
- Final Amount A = $2500
- Number of times interest applied per time period n = monthly = 12
- Time t = 5
We substitute into our formular above
r = n[ (A/P)^(1/nt) - 1 ]
r = 12[ (2500/2000)^(1/(12×5)) - 1 ]
r = 12[ (1.25^(1/60) ) - 1 ]
r = 12[ 1.0037598 - 1 ]
r = 12[ 0.0037598 ]
r = 0.447
Next we convert to percentage
r = 0.447 × 100%
r = 4.47%
The annual interest rate needed to reach the given amount in five years is 4.47%.
Hence, option B) is the correct answer.
Learn more about compound interest here: https://brainly.com/question/13155407
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