Help with Compound Interest Homework Problem

[oceanflavored]

i have five problems on this on my econ test tomorrow. PLEASE HELP! I've looked in my book and can't find anything! thank you :)

Homework Statement

Calculate compound interest:
principal: 65,000
rate: 5.25%
time: 1.5 years

it doesn't say how long it's going to be compounded

Homework Equations

i found this one on wikipedia http://en.wikipedia.org/wiki/Compound_interest :
A = P(1 + (r/n)) ^ (nt)
where,
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
A = amount after time t

and then i found this one...

A = P(1 + r)^t
where,
r = annual interest rate
t = number of years
P = principal amount
A = amount after time t

The Attempt at a Solution

i REALLY tried to calculate this, but i can't get the answer which is supposed to be $5185.36

please help me! i'd reallyreallyreally appreciate it :D

 

[lurflurf]

calculation is
65000*[(1+.0525)^1.5-1]

It is written confusingly
we have
A = P(1 + (r/n)) ^ (nt)
where,
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
A = amount after time t
A = P(1 + (r/n)) ^ (nt)
I = P[(1 + (r/n)) ^ (nt)-1]
I is the interest and
A=I+P
where,
P = 65000
r = .0525
n = 1
t = 1.5
A = 65000*[(1+.0525)^1.5]
I = 65000*[(1+.0525)^1.5-1]

 

[Architeuthis Dux]

Sure, I'd be happy to help! Compound interest can be a tricky concept to understand, so let's break it down step by step.

First, let's clarify the information given in the problem. The principal amount is $65,000, the interest rate is 5.25%, and the time is 1.5 years. However, as you mentioned, it's not specified how often the interest is compounded. This is an important piece of information, as it affects the final calculation.

For now, let's assume that the interest is compounded annually. This means that the interest is calculated once a year. In order to use the first equation you found, A = P(1 + (r/n)) ^ (nt), we need to know how many times the interest is compounded per year (n). Since we are assuming it is compounded annually, n = 1.

Now, let's plug in the values into the equation:
A = 65,000(1 + (0.0525/1))^(1.5*1)
= 65,000(1 + 0.0525)^1.5
= 65,000(1.0525)^1.5
= $71,185.49

This is the amount after 1.5 years if the interest is compounded annually. However, the answer given is $5185.36, so we know that this is not the correct method. This is because the second equation you found, A = P(1 + r)^t, is the correct one to use for annual compounding.

Let's try it using this equation:
A = 65,000(1 + 0.0525)^1.5
= 65,000(1.0525)^1.5
= $71,185.49

As you can see, we get the same answer as before. This is because the first equation is used for when the interest is compounded multiple times within a year. Since we are assuming annual compounding, the second equation is the one we should use.

In order to get the answer of $5185.36, we can use the second equation and solve for the interest (r). This is because the problem gives us the final amount (A) and the other values (P, t). The equation would look like this:
A = P(1 + r)^t
5185.36 =