SOLUTION: I need some help with part B. Also The answer I got for part A is $46,189.24. Is that correct? You have $760,000 in your bank account. The interest rate in your account is 5%.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I need some help with part B. Also The answer I got for part A is $46,189.24. Is that correct? You have $760,000 in your bank account. The interest rate in your account is 5%.      Log On


   

Question 184696: I need some help with part B. Also The answer I got for part A is $46,189.24. Is that correct?
You have $760,000 in your bank account. The interest rate in your account is 5%. Solve for the following:
a. How much interest will you accumulate if interest is compounded annually over the next five years?
b. How much interest will you earn in your account over the next five years with continuous compounding?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Part A.

Actually, you aren't even close. Just do a quick mental sanity check. 10% of 760000 is 76000, so 5% is half of that or 38000. If you only got 5% on your original principal and didn't compound you would get 5 times 38000 in 5 years -- nearly $200K.



Where FV is Future Value, P is Principal, r is the interest rate per compounding period, and n is the number of periods.

For your situation:



(Said his calculator, confidently)

If the Future Value is $969,973.99 on an investment of $760,000.00, then the interest earned is the difference between the two or $209,973.99.

Part B.

Continuous compounding requires a different formula:



Where FV is Future Value, P is Principal, e is the base of the natural logarithms (approx. 2.718), r is the interest rate per time period, and t is the number of time periods.



Again, subtracting the principal, the interest earned is: $215,859.32

So continuous compounding gets you an extra $100 per month over the 5 year period.

John