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using the compound interest table, calculate the compound amount after 5 years for an investment of $7,700 at 6% interest compounded quarterly

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7 Answers

compounding quarterly provides a little bit more interest than annually.  I'll show you both results
 
1)Compounded Annually @6% APR
 
F(0)=$7700 - initial investment
F(n)=Funds after each year compound where n is the year (1,2,3,4,5)
 
F(n)=F(0)*(1.06*n)
F(1)=$8162
F(2)=$8651.72
F(3)=$9170.82
F(4)=$9721.07
F(5)=$10304.44
 
2)Compounded Quarterly @6% APR.  The difference here is that every quarter the present value is compounded by 1.5%.  Therefore, the annual increase is (1.015^4) giving an annual multiplier of 1.0613636  
 
Therefore to get to year 5, we compound F(0) by (1.015^20) =  1.346855 ----> 4 quarters for 5 years
 
F(5)=$7600*1.346855 = $10,370.88    (A wee bit more than annually)
 
 
Fun Fact: Compounding approaches an exponential (F(0)e^(rt)) function as the compounding interval becomes continuous (r is the decimal % and t is given in years)
 
e^(.06*5)=1.3498588   <--Compare to quarterly (1.346855)...not much difference huh?

Comments

Fun Fact: Compounding approaches an exponential (F(0)e^(rt)) function as the compounding interval goes to zero (r is the decimal % and t is given in years)
Thanks.  I switched mental gears from 'interval' to discrete-->continuous.  I type too fast ;-)
the formula is A=P[1+(i/q)]^nq
A=amount you are looking for
P=principal($7700)
i=interest rate expressed as a decimal(6%=0.06)
q=how many times per year the money is compounded(quarterly, or 4)
n=the number of years(5)
0.06/4=0.015
(1.015)^20=1.346855
7700*1.346855=$10,370.78
 
I don't have your compound interest table, but I found one with Google search and will use that.
 
We're investing $7,700 at 6% interest compounded quarterly over 5 years.
 
So we have 4 * 5 = 20 investment periods.
 
The interest for each period is 1/4 the yearly interest, 6/4 = 1.5%/period.
 
In the table for 1.5% and 20 periods the multiplier is 1.347. (Note that the table values are rounded to 3 decimals so the answer with the table will not be as accurate as Parviz's.)
 
So the amount after 5 years (future value) is $7,700 * 1.347 = $10,371.90

Comments

Now, with calculator, there is no need for table.
 
 
 A = 7700 * ( 1 +0.06)^ 5(4)
                           4
    
     = 7700 * ( 1.015)^ 20 =
    
       = 10, 370.78
 
 
Compound interest means you gain interest on all your money, even the interest you've gained so far. For example, a $1,000 loan with compound interest of 10% annually. You would owe $1,100 after the first year, but $1,210 after the second. Why not an even $1,200, because you're being charged interest on last years amount not the principle amount.
 
If you have a 6% interest rate, this refers to your annual interest, but that doesn't mean it's only accrued once a year. If the interest is being compounded quarterly, it means that every quarter (a business term for a quarter of a year, or 3 month) 1.5% interest is being calculated and added to your account. Why 1.5%, because 1.5% per quarter times 4 quarters per year equals 6% per year.
 
So you start with $7,700.00
Then after one quarter you have $7,700 * 1.015 = $7815.50
After two quarters you have $7815.50 * 1.015 = $7932.73
After three quarters you have $7932.73 * 1.015 = $8051.72
And after a full year you'd have $8051.72 * 1.015 = $8172.50
And so on... (for five years)
Compound interest formula: M = P( 1 + I )n

M is the final amount including the principal.

P is the principal amount.

i is the rate of interest per year.

n is the number of years invested.

Applying the Formula

M = 7700( 1 + 0.06 )5
 
M = 7700 (1.06)5
 
M = 7700(1.34)
 
M = 10318

Comments

Have not given, the quarterly compounding into consideration.