SOLUTION: I am stock with this problem please. I'm pregnant I can't sit too long and stand too long.I want to know how to solve and the formula of this. I did try many times I'm still wrong

Question 843046: I am stock with this problem please. I'm pregnant I can't sit too long and stand too long.I want to know how to solve and the formula of this. I did try many times I'm still wrong pls help. Thanks.
What is the future value of $5000 in a bank account for 7 years at 8 percent compounded semiannually?
Found 2 solutions by Theo, jim_thompson5910:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula to use is:

f = p * (1 + r) ^ n
f = future value
p = present value
r = interest per time period
n = number of time periods.

time periods can be yearly or semi-annually, or quarterly, or monthly, or weekly, or daily, or any other period where the compounding of interest occurs.

in general:

you divide the annual interest rate by the number of compounding periods per year.

you multiply the number of years by the number of compounding periods per year.

note that the annual interest rate is the annual percentage rate (called apr) divided by 100.

8% per year annual percentage rate becomes .08 annual interest rate.

in your example, this is how it works.

the formula if f = p * (1 + 4) ^ n

p = $5000.

this is the present amount that you have to invest.

r = .08 / 2 = .04

this is the annual percent of 8%, divided by 100 to turn it into a rate, and then divided by the number of compounding periods per year, which is 2.

n = 7 * 2 = 14

this is the number of years multiplied by the number of compounding periods per year.

your formula of:

f = p * (1+r) ^ n becomes:

f = 5000 * (1.04) ^ 14

you solve for f to get:

f = 8658.382238

This can be rounded to the number of decimal places required by your problem.

If to the nearest dollar, then 8658.
If to the nearest tenths of a dollar, then 8658.4
If to the nearest penny, then 8658.38

the key thing you need to understand is time periods.

The compound interest formula works on time periods.
The time periods are different, depending on the number of compounding periods per year.

The number of time periods in your problem would have been different, depending on the compounding periods per year.

for example:

if the compounding periods were monthly, then the interest rate (r) would have been .08 / 12 and the number of time periods (n) would have been 7 * 12.

if the compounding periods were quarterly, then the interest rate would have been .08 / 4 and the number of time periods would have been 7 * 4.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
We use the formula FV = PV*(1+r/n)^(n*t) where,

FV = future value (currently unknown)
PV = present value (in this case, it's the amount invested, so PV = 5000)
r = interest rate as a decimal (r = 8/100 = 0.08)
n = compounding frequency (semiannual means twice a year, so n = 2)
t = time in years (t = 7 years in this case)

Plug in PV = 5000, r = 0.08, n = 2, t = 7 into the formula to get...

FV = PV*(1+r/n)^(n*t)

FV = 5000*(1+0.08/2)^(2*7)

FV = 8658.38223801402 ... use a calculator here

FV = 8658.38 ... round to the nearest penny

So the future value is $8,658.38
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