MATH SOLVE

2 months ago

Q:
# How long does it take for a deposit of $1400 to double at 2% compounded continuously?

Accepted Solution

A:

Answer:34.66 yrStep-by-step explanation:The formula for interest compounded continuously is
[tex]A = Pe^{rt}[/tex]Data:
P = $1400
r = 2 % = 0.02
Calculations:
(a) Calculate A
A = 2 × 1400 = $2800
(b) Calculate t
[tex]2800 = 1400e^{0.02t}[/tex]
[tex]2 = e^{0.02t}[/tex] Divided each side by 1400
ln2 = 0.02t Took the ln of each side
t = ln2/0.02 Divided each side by 0.02
t = 34.66 yr
It will take 34.66 yr for the investment to double at 2 % interest compounded continuously.
Check:
2800 = 1400e^{0.02×34.66}
2800 = 1400e^{0.6931}
2800 = 1400 × 2
2800 = 2800