Math 12 Help (Find missing variables)

Question

Hello. I'm looking for a variable, "t"

Using the formula

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

We know the following:

A=2025

P=870

r=0.105

n=365

t=?

"I" represents interest earned and is equal to (A - P),

The answer for t is 8.05 but I'm unsure how to reach this number. My work is as follows:

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

2025 = 870(1 + 0.105/365)^365t

2025/870 = (1 + 0.105/365)^365t

2.327586 = (1.000288)^365t

(this is where I am lost)

Where am I making my mistake? I am over-thinking this question, I believe.

Answer 1

Rana, you are doing well, now take natural log of each side

ln(2.327586)=365t*ln(1.000288)

.844831679 = 365t * 0.00028795853

Solve for t, I got

t = 8.03799