SOLUTION: Josh invests $50 weekly for 6 years in his savings account that has a 2.8% interest rate, compounded weekly. How much money will he have after 6 years

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Question 1123270: Josh invests $50 weekly for 6 years in his savings account that has a 2.8% interest rate, compounded weekly. How much money will he have after 6 years
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f = p * (1 + r) ^ n

f is the future value
p if the present value
r is the interest rate per time period
n is the number of time periods

in your problem.

p = 50
f = what you want to find
n = 6 * 52 = 312 weeks
r = 2.8% / 100 / 52 = .0005384615385

formula becomes f = 50 * (1 + .0005384615385) ^ 312

solve for f to get:

f = 59.1441563

the percent interest rate is divided by 100 to get the interest rate per year.

the interest rate per year is divided by 52 to get the interest rate per week.

the number of years is multiplied by 52 to get the number of weeks.


Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Josh invests $50 weekly for 6 years in his savings account that has a 2.8% interest rate, compounded weekly.
How much money will he have after 6 years ?
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This problem is about a future value for Ordinary Annuity saving plan.


Tutor @Theo misread the condition and mistakenly used another formula, which is not relevant to given condition, 
therefore, he obtained incorrect answer. 


The correct formula for the Ordinary Annuity saving plan is


f = p+%2A+%28%28%281+%2B+r%29+%5E+n-1%29%2Fr%29,


f is the future value
p is the weekly payment
r is the interest rate per time period
n is the number of time periods.


In your problem:


time periods are weeks.


p = 50 dollars  
r = 0.028/52   per week
n = 6 * 52 = 312 weeks   (counting 52 weeks in the year)


formula becomes f = 50+%2A+%28%28%281+%2B+0.028%2F52%29+%5E+312-1%29%2F%28%280.028%2F52%29%29%29 = 16982.


Josh will have $16982 in his saving account in 6 years.


Interesting, that his total direct investment will be only  $50*52*6 = $15600.

The rest is what the account will earn due to compounded percentage.

Solved.

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On Ordinary Annuity saving plans see the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
in this site.