Math help...........?

Question

How much moeny would you have in 4 years if you bought a $3,000 certificate that pays 6% interest compounded daily?

Answer 1

If such a bond existed, I would cautious, as it's probably a "junk bond." In anycase, assuming that the bond managed to actually pay it back, this is how it would work.

The formula for compound interest is:
FV = PV( 1 + i )^n
FV - Future Value of the bond
PV - Present Value of the bond
i - interest rate
n - number of times it is compounded.

First, let's see what we know. We know that the Present Value (PV) of the bond is $3,000. And we also know that i, the interest is 6%. For the sake of this formula, we must convert this as a decimal, which would make i = 0.06.

Now, we need to figure out what n is. Every year is 4 years, and each year has 365 days. 4 * 365 = 1460. So, let's plug it into the calculator!
FV = 3000 (1 + 0.06)^1460
FV = 3000 * 1.06^1460
FV = 3000 * (8.8422 x 10^36) (really big number)
FV = 2.6526 x 10^40

Basically, it would 265 with 38 zeroes following it.

Now, I'm hoping that you simply read it wrong, that the interest may compound daily, but the Annual Percentage Rate is actually 6%

Answer 2

The formula:

Total amount = P(1 + i)^n

Where P = original amount = $3,000

i = interest rate 6%

n = number of periods, here is where you have to be careful. Let's assume 365 days in a year (leap year is different). So we have n = 365*4 days.

Now we revisit i ,

To solve the problem in like units, we need to divide i by 365 for the daily interest rate.

Thus the equation is:

Total amount = $3,000(1+ 0.06/365)^(365*4)

Total amount = $3,000(1.0001644)^1460

Total amount = $3,000(1.2744)

Finally.

Total amount = $3,813.67

If you compound continuously, the answer won't be much more.

Here is a little extra information.

The same compound interest formula

Where n approaches infinity, will give us the value of e, the base of natural logarithms.

as n approaches infinity, e = (1 + i/n)^n = 2.71828...