Question

функция Паузы Exercise 3.7 Aidana deposits 100 in a banks account every day for 3 years. If i = 0,08 convertible quarterly, how much has she accumulated at the time ot the last deposit?

Answer 1

Data given in the question,

1. I⁽⁴⁾ = 8%
2. Deposit Amount = 100
3. Periodicity = every day i.e. 365 for 3 years.

Calculation of Equivalent Effective Annual Interest Rate,

          i = (1+ i⁴/4)⁴ – 1 = (1.02)⁴ – 1 = 8.243%

Calculation of Nominal rate compounded daily (using the same formula as above),

                             I³⁶⁵ = 7.922%

Now, Calculation of the final maturity amount,

Maturity Amount = 100*365*3*(1+i³⁶⁵/365)^365*3

                  

                            = 109500*(1.000217)^365*3

                             = 138872.53 Approx.

The answer given above is in approximate value due to the under-root and power function being used on a calculator.

The exact answer using the excel-spread sheet is = 123618.48