Question

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

Answer 1

.01/12 + 1 = 1.0008333333


6000 *(1.000833333)^120= 6630.75

=============================
dx/dt2 = e^.07t
ln 2 = .07 t
t = 3.35

Answer 2

.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.

Answer 3

sorry, did typo with calculator the first time I did problem 2

Answer 4

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