A new savings account offers 6 percent annual interest compounded ever

Question

A new savings account offers 6 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?

A. $80.00
B. $84.40
C. $360.00
D. $6,360.00
E. $6,365.40

Kudos for a correct  solution .

balamoon · Answer

Solution -

At the end of the first 6 months, the interest earned is (1/2)*6000*(6/100) = 180. (6 months is 1/2 in the equation since 6% is a yearly rate, not for six months).

Since the interest is compounded, the second six months of the year is getting interest on original and first six months interest i.e.,6180.

The interest earned during the final 6 months of the year is (1/2)*6180*(6/100) = 185.4

The total balance at the end of the year is 6000+180+185.4=6365.4
ANS E

ENGRTOMBA2018 · Answer

2 ways to do this:

Method 1:

Compund interest formula: Final amount = P*(1+(R/n)%)^n where n =2 for annual interest compounded semi annually.

Thus the final amount = 6000(1+3/100)^2 = 6365.4, E is the correct answer.

Method 2:

We know that compound interest is interest accumulated on the previous periods' simple interest.

In other words,

Interest earned for the 1st 6 months = 6000*3*1/100= 180. Amount after the first 3 months = 6000+180=6180$

Now, again for the remaining 6 months = 6180*3*1/100= 185.4$ ---> Amount after 6 months = 6180+185.4 = 6365.4. E is the correct answer.

TimeTraveller · Answer

Interest rate = 6 (compounded half-yearly), so 6/2 = 3%.

Balance at the end of one year = 6000 (1+3/100)^2 = 6000 (1.03)^2 = $6365.4

Ans (E).

JJo · Answer

Annual interest = 6%, compounded every 6 months, hence 3% for 1st 6 months and 3% for 2nd half

amt. after 1st half = 6000+3%of 6000 = 6000+180 = 6180
amt. after 2nd half = 6180+3%of 6180 = 6180+185.4 = 6365.40

Ans. E. $6,365.40

VenoMfTw · Answer

Since total amount can't be less than the initial value 
eliminate options A B and C

6% annual interest compounded every 6 months --- So interest for every 6 months is 3%

3% or 6000 = 180 for one cycle
for two cycles 180+180+some amount since it is a compounded interest.

thus interest must be greater than 360 ---> thus the total sum must be greater than 6360

Leaves us with only Option(E).

cutegirlsimran · Answer

6 percent annual interest compounded every 6 months so

3% Interest Rate and amount is 6000

After 6 months we get 6000 * 0.03 i.e 180
so Amount becomes 6000 + 180 = 6180

Again after 6 months we get 6180 * 0.03 = 185.40

Total Amount After 1 Year is 6180 + 185.40 = 6365.40

Bunuel · Answer

800score Official Solution:

The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.06) (1/2) = $180. (Note: the 6 months are “1/2” in the equation since 6% is a yearly rate, not a bi-yearly one).

Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,180. The interest earned during the final 6 months of the year is $6,180(.06)(1/2) = $185.4. Therefore, the total balance is the original amount ($6000) + $180 + $185.40 = $6,365.40.

The correct answer is E.

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A new savings account offers 6 percent annual interest compounded ever

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