|
Question 1139585: Compute the future value after one year for $100 invested at 4% interest compounded quarterly. what simple interest rate will yield the same amount in one year
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula for compound interest 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.
when you are compounding quarterly for 1 year, .....
r = 4% per year / 4 = 1% per quarter = .01
n = 1 year * 4 = 4 quarters.
the formula becomes f = 100 * (1 + .01) ^ 4 = 104.060401.
the interest earned is 104.060401 - 100 = 4.060401.
the simple interest rate is 4.060401 / 100 = .04060401.
that's a simple interest rate of .04060401 per year.
the simple interest formula is i = p * r * n
when dealing with quarters, the annual interest rate of .04060401 is divided by 4 to get a quarterly interest rate of .0101510025.
the simple interest formula becomes i = 100 * .0101510025 * 4.
.0101510025 is the interest rate per quarter and 4 is the number of quarters.
solve for i to get i = 100 * .0101510025 * r = 4.060401.
that's the same interest as we got using the compound interest formula.
this is as expected since we derived the simple interest rate formula from the results of the compound interest rate formula.
your solution is that the simple interest rate that will yield the same amount as was derived using the compound interest formula is .04060401.
a simple interest rate of .04060401 per year is equal to a simple interest rate of 4.060401% per year.
percent rate is divided by 100 to get rate.
rate is multiplied by 100 to get percent rate.
if your answer is rate only, then .04060401.
if you answer is rate percent, then 4.060401%.
that'a an annual interest rate.
the quarterly simple interest would be that divided by 4.
|
|
|
| |
