Question

Lifesaver
amount=principal * (1+(Rate/T))^T

interest rate: 4.25%
interest compound quarterly: 12
principal: $1000


what is the interest?

Answer 1

You have the formula right there. Are you having trouble applying it?

Answer 2

yeah im having trouble applying it to get the amount of interest gained

Answer 3

What have you tried?

Answer 4

i used the I=Prt formula because that is the one for interest but i think i'm doing it wrong or........it could be the wrong formula

Answer 5

The formula is right. You just need to apply it. How do you think you need to apply it to the numbers given?

Answer 6

find out what the amount first

Answer 7

what the amount is first*

Answer 8

Well, that's going to be the end result of our process of applying the formula. Where do the numbers you gave go? Post your version of the formula with the numbers inserted for the variables.

Answer 9

(1000)(1+(.0425/12)^12

Answer 10

That's very close. The problem says the interest in compounded quarterly. How would you change your expression to account for that?

Answer 11

Yours would be right if it was compounded monthly.

Answer 12

quarterly wouldn't it be (4/12)

Answer 13

There are 4 quarters in a year (12 months), yes. So how would you account for that in the expression you posted?

Answer 14

How long is t if you're compounding quarterly?

Answer 15

expression would be: 1000*(1+(.0425/12))^(4/12)

Answer 16

No. How long is t (in months) if you're compounding quarterly?

Answer 17

per 3 months

Answer 18

Right. And how many 3-month time periods are we interested in. (I can't really tell what "interest compound quarterly: 12" means in your problem statement, so I'm going to have to trust your answer on this.)

Answer 19

ohhh that is wrong it should be interest compound: 12

i was reading another problem by mistake...Sorry!!

Answer 20

Well, we can finish this problem so you can understand the formula. Should we compound the interest over 12 months (4 quarters) or 12 quarters?

Answer 21

12 months ( 4 quarters)

Answer 22

Okay, so adjust the expression you posted to include that. Post the new expression.

Answer 23

(1000)(1+(.0425/12)^(4)

Answer 24

Closer. The R/T part is not right yet. T in this problem is 3 months, so we need to figure out what the quarterly rate would be, not the monthly rate.

Answer 25

1+(.0425/3)^(3/12)

Answer 26

Each T represents a 3-month period. So there are 4 of them in a year. So T=4.

Answer 27

The tricky part of these interest problems is making sure you understand exactly what time period is being used. Then convert the rate to that time period, and figure out how many time periods you have to compound the interest for.

The R/T term is converting the rate from some stated rate (per some arbitrary time period) to the rate you want to use (for your target time period, 1 quarter in this example). They gave the rate as a yearly rate (per 4 quarters). We want the quarterly rate, so we divide it by 4 (4 quarters per year).

The T in the exponent is the number of time periods to compound interest over (4 quarters in this example).

Answer 28

i get it now thanks for the help!!

Answer 29

So, the approach to solving these problems is:
1. Determine the base time period they're asking for (how often the interest is to be calculated)
2. If the rate wasn't expressed in that time period, convert it to that time period.
3. Determine how many time periods to calculate the interest for.

In our example:
1. compound quarterly, so each T represents 1 quarter.
2. 4.25% yearly rate = 1.0625% quarterly rate
3. 1 year is 4 of our time periods, so T = 4.

Total = 1000 * (1 + 1.0625%)^4 = $1043.18.