jeff deposits $2300 at 3.13% intrest compounded weekly. what will be his ending balance after one year?

Question

 jeff deposits $2300 at 3.13% interest compounded weekly what will be his ending balance after one year 

Answer 1

Hi Asiya,

 

Let's begin by recalling the Compound Interest formula: 

    A = P(1 + (r/p))^pt (Compound Interest formula)

 

Now let's identify the variables in the formula:

    A = future amount

    P = initial amount

    r = annual interest rate

    p = number of annual compounded periods

    t = number of years

 

Finally, let's plug in the given values for these variables and calculate the balance after one year:

    A = (2300)(1 + (0.0313/52))^(52)(1)

    A = (2300)(1 + 0.000601923076)⁵²

    A = (2300)(1.000601923076)⁵²

    A = (2300)(1.03178528)

    A = 2373.106144

    A = $2373.11 (rounded to nearest penny)

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

The equation for compound interest is A(t)=P(1+r/n)^nt, where:

 

A(t) = amount after t years

P = principal amount

r = interest rate

n = number of times the interest is compounded

t = number of years

 

So for your problem, since the interest is being compounded weekly, we need to know that there are 52 weeks in a year. The interest rate will need to be written as a decimal, so 3.13% is r=0.0313. It's asking for the amount after 1 year, so t=1. Thus, the function should be:

 

A(1) = 2300(1+0.0313/52)⁵²⁽¹⁾

A(1) = 2300(1.0006)⁵²

A(1) = 2300(1.0318)

A(1) = 2373.11

 

Jeff should expect his ending amount after one year to be $2373.11.

Answer 3

Asiya:

 

You have two correct answers.  Let me try to explain in words what they did.

 

First, remember that when you are asked for a future value, you will multiple.  When you are asked for a present value you will divide.  in other words, C(some cash number) x 1+r^n, where r is the interest rate and n is the number of periods.

 

 

In compounding, you divide the interest rate, in this case, 3.13% by the time periods.  In this case, it is 52 weeks.  But if it were monthly compounding (which is very common), you would divided by 12.  Then, you add 1 to the resulting fraction.  In this case, .0313/52=.0006 and add 1, you get 1.0006.  You take this number to the power of the number of periods, in this case 52, but in monthly compounding, it would be 12.  As shown in the other answers, 1.0006^52 = 1.0318. 

 

The other thing i recommend is to find a way to do a proof of your work.  In this case, you can use simple interest, just multiply $2300 x 1.0313 and you get 2371.99.  You know interest compounded weekly must be higher than simple interest, but this assures you that you are in the right ballpark.  When you are doing these kind of calculations (taking something to the 52d power), it is easy to get confused.  This will make sure that you have a sensible answer.  It only takes a second to do.