Question 1147218: Determine the amount of money that will be accumulated in an account that pays compound interest, given the initial principal of $27,800 invested at 2.97% annual interest for 9 years compounded
(a) daily (n=365);
(b) continuously.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! discrete compounding formula is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods
continuous compounding formula is f = p * e ^ (r * t)
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods
using the discrete compounding formula, your problem becomes:
f = 27500 * (1 + .0297/365) ^ (9 * 365) = 35,926.49804.
using the continuous compounding formula, your problem becomes;
f = 27500 * e ^ (.0297 * 9) = 35,926.88872.
we could also have done:
f = 27500 * e ^ (.0297/365 * 9 * 365) = 35,926.88872.
since the compounding is continuous, it doesn't matter what time periods we use as long as we're consistant, i.e. r = annual interest rate / number of compounding periods per year paired with n = number of years * number of compounding periods per year.
also note that daily compounding gets pretty close to continuous compounding.
the more compounding periods per year you get, the closer you get to continuous compounding results.
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