Question

Suppose you deposited $10,000 in a savings account earning 3.9% interest compounding daily. How long will it take for the balance to grow to $21,000? Answer in years rounded to one decimal place.

Answer 1

Lets Assumed 3.90% of interest rate is Annual Saving Bank Account Interest Rate,
Deposited Amt on Starting date Is $10,000/-,
Interest Compounding daily Basis is i.e.3.90%,
Maturity Amount will be $ 21,000/-,
Then Found Out How Many Year(?) required under daily basis compounding of Interest....

Formula For Calculation of Growth Of Amount :-

A = P (1 + r/n)nt

where A = Growth Of Amount
         P = Principle Invested
         r = Interest Rate
        n = No.Of Compounding Annually or Say Conversions
        t = times (in years)

now we Put figure into formula,

$21,000 = $10,000(1+3.90/360)(360*t)

Time Duration, Solve for t based on Log Table,

t = ln(A/P) / n[ln(1 + r/n)] = [ ln(A) - ln(P) ] / n[ln(1 + r/n)]
= In($21000/$10000) / 360[In(1 + 3.90/360]
= [In($21000) - In($10000)] / 360[In(1+3.90/365]
= 19.03 Years (Appx 19.00 Years)

(Note : Interest Compounded dailly Basis means Added At the end of each day & 360 days into 1 Year)
[Reconciliation for Understanding Only:-
A= $10,000(1+3.90/360)(360*19.03) = $21,004.04]