Math problem!!!?

Question

Find the new balance for $1000 left on deposit for 6 months at 4% interest compounded quarterly.


Do you use a formula to find the answer? Please help!!!

Answer 1

Typically, interest rates are given on an annual basis, not for the period at which the interest is compounded. Therefore, a quarter's interest should be 1% ($10 for the first quarter).

So after one quarter your principle is $1010.
After the second your principle is $1020.10 (because 1% of the principle now adds $10.10).

Answer 2

If interest compounded annually on the amount P

A = P(1+r)^n, where r is interest rate, n is number of years and A is the new balance

when it is compounded quaterly , r = r/4 and n = 4 (quarters)

A = P(1+r/4)^4

If it is only 6 months , then n = n/2 = 4/2 =2

A = P(1+r/4)^2

here P = 1000, r = 4/100 = 0.04

A = 1000(1+ 0.04/4)^2

A= 1000(1.01)^2 = 1020.10

so new balance = $1020.10

Answer 3

Because the interest is compounded quarterly, we must first find the quarterly interest rate.

Assuming the 4% interest is an annual interest rate, the quarterly interest rate is 4% divided by 4 = 1%.

After one quarter, we will receive 1% interest. $1000 x 1% = $10. We also have our original deposit, so after one quarter we will have $1010. This is the new amount that should be used to calculate interest going forward.

After the second quarter, we receive another 1% interest. $1010 x 1% = $10.10. (The compounding accounts for the additional $0.10 of interest we receive in the second quarter.) After two quarters, we will have $1020.10.

As for a formula:

New Balance (NB) = Original Balance (OB) + Interest (I).
I = OB * Quarterly Interest Rate (QIR).

Thus,

NB = OB + (OB * QIR)

Factoring OB, we have

NB = OB x (1 + QIR)

In our case, after one quarter, NB = $1000 (1 + 0.01) = $1000 (1.01) = $1010.

To compute the balance after the second quarter, in our formula, we must use our New Balance after the first quarter as the Original Balance.

Thus, substituting OB x (1 + QIR) for OB,

NB = OB x (1 + QIR) x (1 + QIR).

Combining the two terms of (1 + QIR), we have

NB = OB x (1 + QIR)^2.

For example, after two quarters, we have NB = $1000 x 1.01^2 = $1000 x 1.0201 = $1020.10.

After X quarters, we have NB = OB x (1 + QIR)^X.

Answer 4

okay there is a formula. It's the exponential growth formula A = P(1 + i)^n [^n is to the power of n] where P= principle [$1000], i=interest as a decimal [0.04] and n = number of periods. [2 - Six months is two quarters] Therefore, A= 1000(1+0.04)^2 = 1000 x 1.04^2 = 1000 x 1.0816 = $1081.60

Answer 5

Yeah, for the formula you type into your calqualator 1000*(times)0.04 (4 percent) 6 times but you have to add up the number everytime. The first time you do it you will get that 1000*0.04 is 40 but you have to add that to 1000 to get 1040 and then type it in again however many times they get interest added to there account.

Hope this helps!

Answer 6

The formula to find interest is
A=P(1+r)^n
P=principle amount
r=Rate is the % of interest in a decimal
n=years
After 6 months compounded quarterly, it would be
P=1000(1+(0.04/4))^(0.5x4)
=$1020.10

If it was compounded monthly then it would be
P=1000(1+(0.04/12))^(0.5x12)
and so forth..

Answer 7

You need this formula:
Compound Interest
A= P ( 1+r / n ) ^ nt
A= total amount accrued
P= initial investment
r = rate as a decimal
n= amount of times compounded a year
t= amount of time money is invested in years

Your Question:
A= 1000 ( 1+0.04 / 4) ^ 4*0.5
= 67.6
So the 67.6 is your interest.
Hence new balance is 67.6 + 1000 = $1067.6

Hope this helps!

Answer 8

4% interest is added each 3 months (each quarter)
So after 3 months,
1000 + (0.04 x 1000)= 1040
And then for months 3 - 6
1040 + (0.04 x 1040)= 1081.6

so you'd have $1081.6