SOLUTION: Someone please help me with the following problem: Suppose $5000 is invested at interest rate k, compounded continuously and grows to $6954.84 in 6 years. (a) Find the intere

Question 169194: Someone please help me with the following problem:
Suppose $5000 is invested at interest rate k, compounded continuously and grows to $6954.84 in 6 years.
(a) Find the interest rate

(b) Find the exponential growth function

(c) Find the balance after 10 years

(d) Find the doubling time

Thanks.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Someone please help me with the following problem:
Suppose $5000 is invested at interest rate k, compounded continuously and grows to $6954.84 in 6 years.
:
The continuous interest formula: = A
Where:
P = initial amt (5000)
r = interest rate in decimal form (k in this problem)
t = time, in years (6yrs)
A = final amt (6954.84)
:
(a) Find the interest rate
= 6954.84
=
:
= 1.390968; divided both sides by 5000
:
6k*ln(e) = ln(1.390968); find the nat log of both sides
:
6k = .33; nat log of e is 1
:
k =
k = .055, 5.5% interest
:
Check on a calc: enter: 5000*e^(6*.055) = 6954.84
>
:
<
(b) Find the exponential growth function
A =
;
:
(c) Find the balance after 10 years
On a calc enter = 8666.27

(d) Find the doubling time
= 10000; we want to find t here
:
=
:
= 2;
:
.055t*ln(e) = ln(2); find the nat log of both sides
:
.055t = .693;
:
t =
t = 12.6 yrs
:
:
Check on a calc: enter: 5000*e^(12.6*.055) = 9998.53 ~ 10000
>

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