Compound interest again?

Question

What is $270.93 invested per month for 48 months @ 8% per annum compounded monthly? Plz show calculations

Answer 1

Amt = Principal (1 + i)^n

where i is periodic interest rate and n is number of periods.

You must present the interest rate in monthly terms as shown below because of the monthly compounding.

Amt = 270.93(1 + 0.08/12)^48

Amt = 270.93 * 1.3756661

Amt = $372.91
.

Answer 2

Robert, yours is obviously wrong. What you have is the amount at the end of 48 months from a single deposit of $270.93 earning at 8% compounded monthly.

Justingeneral, yours is amortization, like payment for a car loan. Your answer is the principal of a loan to be paid month at the rate of 8% for 48 months. Compounding is not applied at all. Look, 48 x $270.93 (= $13,004.64) alone is already almost equal to your answer.

The original question is asking what will be the total accumulated amount if $270.93 is deposited every month for 48 months earning 8% compounded monthly.

It should be something like:

P = S [1 + 1.006666^1 + 1.006666^2 + 1.006666^3 + ..... + 1.006666^47]

Observe: the first deposit earned interest 47 times. The last deposit earned no interest. The same last deposit can be express too as 1.0066666^0 which is also equal to "1".

where:
P = total accumulated amount at the end of 48 months
S = is the monthly deposit (the guy is saving)
1.0066666 = 1 + 0.08/12 >>>> (12 here is number of months in a year. Because 8% is the interest for a year, so it has to be divided by 12 months)

With that equation about, the total accumulated amount will be $15,266.86.

Answer 3

Robert L is obviously wrong here.

He failed to take into account that the $270.93 is invested for a period of 48 months. He calculated the Interest just for the first month. Alas! That isnt the way to do it.

When I entered the values into money software, here's what I got.

$270.93 invested per month for 48 months @ 8% per annum compounded monthly = $13,013.04

Answer 4

RobertL is right on the money.