Question

suppose that $28,000 is deposited in an account and the balance increases to $34,542.99 after 3 years. How long will it take for the account to grow $70,049.67? Assuming continuous compounding.

it will take about _ years for $28,000 to grow to $70,049.67

Answer 1

Solution:

Let k be the rate (compounded continuously) at which Principal is increasing.

P(t) Pockt

where

P₀ = Principal = $28000

k = growth rate(compounded continuously) = ?

P(t) = Amount at given time t.

In 3 years, balance increases to $34542.99

34542.99 = 28000

$\small \frac{34542.99}{28000}=e^{k\times 3}$

$\small 1.2337=e^{k\times 3}$

$\small ln(1.2337)=ln(e^{k\times 3})$

0.21 = 3k

k = 0.07

Now,

$\small 70049.67=28000e^{kt}$

$\small \frac{70049.67}{28000}=e^{0.07t}$

$\small 2.5=e^{0.07t}$

$\small ln(2.5)=ln(e^{0.07t})$

0.9163 = 0.07t

t = 13.09

It will take about 13 years for $28000 to grow to $70049.67.