I keep getting the problems wrong? Please help
James deposits $6000 into a savings account which pays 1% per annum. If the account compounds monthly, find the amount in the account after 10 years.
(ive gotten 6631 but that's wrong)
Nick deposits $8,000 into a savings account which pays 7% per year. If the account compounds continuously, find the time it takes to double his investment. (Round your answer to the nearest whole year.)
(ive gotten 10 but its also wrong
.01/12 + 1 = 1.0008333333
6000 *(1.000833333)^120= 6630.75
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dx/dt2 = e^.07t
ln 2 = .07 t
t = 3.35
.01/12 + 1 = 1.0008333333
6000 *(1.000833333)^120= 6630.75
=============================
dx/dt= .07 x
dx/x = .07
so
ln x = .07 t
x = k e^.07 t
so
2 = e^.07t
ln 2 = .07 t
t = 9.90
so I agree with you if you round off but I do not know what accuracy you are supposed to have.
sorry, did typo with calculator the first time I did problem 2
not sure what's with all the derivatives, but after 10 years he has
6000(1+.01/12)^(12*10) = 6630.75
for the other, we have
e^(.07t) = 2
.07t = ln2
t = ln2/.07 = 9.9 years
To solve these problems, we need to use the compound interest formula and the continuous compound interest formula, respectively.
1) For the first problem:
The compound interest formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = the future amount in the account
P = the principal (initial amount)
r = the interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the time in years
In this case, the principal (P) is $6000, the interest rate (r) is 1% (or 0.01 as a decimal), the number of times interest is compounded per year (n) is 12 (monthly compounding), and the time (t) is 10 years. Plugging in these values into the formula, we have:
A = $6000(1 + 0.01/12)^(12*10)
A ≈ $6000(1.00833333333)^120
A ≈ $6000(1.12682503021)
A ≈ $6760.95
Therefore, the amount in the account after 10 years would be approximately $6760.95.
If you got a different answer, please double-check your calculations to ensure you've used the correct formula and performed the calculations accurately.
2) For the second problem:
The continuous compound interest formula is given by:
A = Pe^(rt)
Where:
A = the future amount in the account
P = the principal (initial amount)
e = the base of natural logarithms (approximately 2.71828)
r = the interest rate (as a decimal)
t = the time in years
In this case, the principal (P) is $8000, the interest rate (r) is 7% (or 0.07 as a decimal), and we want to find the time (t) it takes for the investment to double. We can set up the equation as follows:
2P = Pe^(0.07t)
Dividing both sides by P, we get:
2 = e^(0.07t)
Taking the natural logarithm of both sides, we have:
ln(2) = 0.07t
Now, we can solve for t by dividing both sides by 0.07:
t = ln(2) / 0.07 ≈ 9.90
Rounding to the nearest whole year, the time it takes for Nick's investment to double is approximately 10 years.
Again, please double-check your calculations to ensure you're using the correct formula and performing the calculations accurately.