Question

Please with formula and process:

What is the time required to double $ 5,0000 at 4.8% interest? Which of the following calculations provides higher performance? Basically your answer.

a) 12% per year
b) 12% semi-annually
c) 12% quarterly
d) 12% daily

Answer 1

Initial Deposit = $50,000
Interest Rate = 4.8%
We have to compute number of years it will take to double this investment.

In financial terms,
PV = $50,000
FV = $100,000
Interest Rate = 4.8%
We have to find no of years.

By using the formula to calculate Number of Periods in excel. The formula is
NPer(Rate, PMT, Present Value, Future Value, Type)
where,
Rate = Interest Rate
PMT = Periodic Payments
Type is 0 if PMT are made on the end of year and 1 if the payments are made at the beginning of year.
Using the formula
N = 15 (rounded off)

So it will take 15 years to double the investment.

12% daily compounding will provide higher performance as the compounding interval will be early and no of compounding periods will be more. The effective annual interest rate will be :

Effective Annual Interest Rate = [1 +(i/n)]n – 1
where,
i = interest Rate
n = Number of periods

No of semi annual periods in a year = 2
No of quarterly periods in a year = 4
No of daily periods in a year = 365

Using the formula,
a) 12% per year = [1 +(0.12/1)]1 – 1 = 12%
b) 12% semi annually = [1 +(0.12/2)]2 – 1 = [1 +0.06]2 - 1 = 12.36%
c) 12% quarterly = [1 +(0.12/4)]4 – 1 = [1 +0.03]4 – 1 = 12.55%
d) 12% daily = [1 +(0.12/365)]365 – 1 = [1 +0.00032877]365 – 1 = 12.75%

So 12% daily compounding provides higher performance.