The value of Christine’s 401 ( k ) after the 360 t h deposit ( 30 years), if Christine contributes $ 100 each month to her 401 ( k ) and the per annum rate of return is assumed to be 8 % compounded monthly.
The value of Christine’s 401 ( k ) after the 360 t h deposit ( 30 years), if Christine contributes $ 100 each month to her 401 ( k ) and the per annum rate of return is assumed to be 8 % compounded monthly.
To calculate: The value of Christine’s 401(k) after the 360th deposit (30 years), if Christine contributes $100 each month to her 401(k) and the per annum rate of return is assumed to be 8% compounded monthly.
Expert Solution & Answer
Answer to Problem 89AYU
Solution:
The value of Christine’s 401(k) after the 360th deposits is $149035.94
Explanation of Solution
Given information:
Christine contributes $100 each month to her 401(k) and the per annum rate of return is assumed to be 8% compounded monthly.
Formula used:
Theorem Amount of an Annuity:
Suppose that P is the deposit in dollars made at the end of each payment period for an annuity paying i percent interest per payment period. The amount A of the annuity after n deposits is
A=P(1+i)n−1i
Calculation:
Christine contributes $100 each month to her 401(k) so P=$100
Per annum rate of return is 8%
Per month rate of return is 8%12=0.6667%
The number of deposits n=360
By using the theorem of amount of an annuity
The value of money after 360th deposits =100(1+0.006667)360−10.006667
=100(1.006667)360−10.006667
=10010.935729658−10.006667
=1009.9357296580.006667=149035.94
Therefore, the value of Christine’s 401(k) after the 360th deposits is $149035.94
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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