Question

Michael invests USD 20 000 at 9.6% p.a. compounded monthly.

How long will it take for his investment to reach USD 25 000?

Answer 1

To determine how long it will take for Michael's investment to reach $25,000, we can use the formula for compound interest. By substituting the given values into the formula and solving for t, we find that it will take approximately 5.31 years for the investment to reach $25,000.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the future value of the investment ($25,000)

P is the principal amount (initial investment of $20,000)

r is the annual interest rate (9.6% or 0.096)

n is the number of times interest is compounded per year (12, since it's compounded monthly)

t is the number of years

Substituting the given values into the formula, we get:

$25,000 = $20,000(1 + 0.096/12)^(12t)

Now, we can solve for t by isolating it:

(1 + 0.096/12)^(12t) = 25,000/20,000

(1.008)^(12t) = 1.25

To solve for t, we can take the logarithm of both sides:

12t = log(1.25) / log(1.008)

t = (log(1.25) / log(1.008)) / 12

Using a calculator, we find that t is approximately 5.31 years.

Answer 2

Given :

A = 25000

P = 20000

r % = 9.6 % = 0.096

n = 12

To Find :

The time taken say t.

Solution :

We know, compound interest is given by :

`A=P(1+(r)/(n))^(n.t)`

Taking log both sides :

`A=P(1+(r)/(n))^(n.t)\\\\log\ (A)/(P)= n.t* log( 1+(r)/(n))\\\\t =(1)/(n)* (log\ (A)/(P))/(log(1+(r)/(n)))\\\\\\t=(1)/(12)* (log\ (25000)/(20000))/(log(1+(0.096)/(12)))\\\\\\t=2.33\ years`

Hence, this is the required solution.