Question

Landon opened a savings account with a deposit of $3,786.45. Nine years later, the balance in the account is $5,135.29. If the interest rate is 3.4%, how often does the interest compound?

Answer 1

@ganeshie8

Answer 2

For a compound interest calculation the formula is total = princ*(1+Rate)^years
We know the rate is 3.4 % but we need to know the compounded rate
Solving this for rate
log(1 + rate) = {log(total) -log(Principal)} ÷ Years
log(1 + rate) = (log (5,135.29) -log(3,786.45) / 9
log(1 + rate) = (3.7105649741 - 3.5782322263) / 9
log(1 + rate) = 0.1323327477 /9
log(1 + rate) = 0.014703639
1 + rate = 1.0344360295
rate = .0344360295
or 3.44360295

Now we have to determine what compounding rate is needed to change 3.4% to 3.44360295%

Answer 3

which are annually, daily, quarterly and monthly right?

Answer 4

Compounded rate = (1 + [rate/n])^n where n is number of compounding periods per year Compounded rate = (1 + .034/n)^n
Solving by trial and error
Semi-Annual Compounded rate = (1 + .034)^n
Compounded rate = (1.017^2) = 1.034289
rate = 3.4289 % which is lower than 3.44360295% so we need to compound more frequently

Quarterly Compounded Rate
Compounded rate = (1 + .034/4)^n Compounded rate = (1+ 0.0085) ^ n = 1.034436 rate = 3.4436% So it must be compounded quarterly

Yes it's just that simple LOL

Answer 5

So the Answer is Quarterly?

Answer 6

And to answer your question compounding can be done
semi-annually, quarterly, monthly, daily, or continuously.

Answer 7

Yes the answer is quarterly. Of course if you need to show the math to back up your answer, just copy and paste my 2 postings.

Answer 8

Thank you for the help!!

Answer 9

u r welcome Cjones