Math Compounded Interest Questions?
A = P(1+r/n)^n/t
A = account after t years
P = amount invented/deposited
r = decimal annual interest rate
n = number of times compounded
t = number of years
1) Patty deposits $1000 that pays 9% (.09) interest compounded quarterly so how long will it take for the account to earn $1000 interest?
2) Mary invests $2300 at 7.5% (.075) interest compounded semiannually so how long will it take for the money to double?
Answers:
I think there's something wrong with your formula. It seems to me like it should be ^(n*t) or ^n^t not ^n/t.
1) After she gets $1000 in interest, the total amount will be $2000, so A = $2000, giving you:
2000 = 1000*(1+.09/4)^(4*t)
Divide both sides by 1000 to get
2 = (1.0225)^(4*t) which is the same as
2 = (1.0225)^4 ^t which is the same as
2 = 1.09308331878906 ^ t
To solve for t, take the log(2) and divide by log(1.09308331878906) to get 7.78795742838354.years.
Since the interest is paid quarterly, you must round UP to the next quarter year, so that would be 8 years.
2) $4600 = $2300(1+.075/2)^(2*t). Solve the same way and you get 9.41418599738467, which rounded up to the next half year is 9.5 years.
Here's a little trick you can use to see if you answer seems right. For moderate interest rates (up to about 14% or so), the number of years it takes for an investment to double will be approximately 72 divided by the interest rate. It's not exact, but it's close. So if the interest rate is 6%, your answer should end up somewhere close to 12 years. If you get 15 years or 8 years or something like that, you've calculated something wrong.
You can also figure this.:
Principal x rate = t x 365 (days of the year)= t x (number of days at that rate)= That will give you the quarterly amount paid...
1000 x .09 = 90 / 365 = 0.2465753425 x 90(number of days of 1 quarter) =22.19178082 x 4 (quarters) = 88.76712329 total paid for 1 year.x 11 years =976.4383562 .
1000-976.44= 23.56
88.77 ] 23.56= 3.767826825 (almost 4 months...)
so it would take you 11 years and 3 months and 1 week to get to $1000
2300 x .075 = 172.5/ 365= 0.4726027397 x 180=85.06849315 x 2 = 170.1369863 x 13=2211.780822
2300-2211.78= 88.22
85.01/180= 0.4722777778 x 187= 88.31594445
it would take 13 years and 6 months and 1 week.
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finance.cch.com/tools/calcs.as...
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