Advance Finance

Advance Finance

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Advance Finance
Question 1: Periodic Interest Rates
Calculating Periodic Rate and Effective Annual Interest Rate
Applied Formula by Fouque and Papanicolaou (2011):
Effective interest rate per period, (i) = ( 1 + ( r / m ) )m – 1
Effective interest rate for t periods, it = ( 1 + i )t - 1 or a single equation it = ( 1 + ( r / m ) )mt - 1.
The rate per compounding period P = R / m, in percent.
Where: r = R/100 and i = I/100 (p. 124)
Filled Table (Rounded to two decimal places)

Period
Annual percentage rate (APR)
Compounding per Period (m)
Periodic rate/
Periodic Interest Rate (P)
Effective Annual Rate
(i)
Semiannual
9%
2
4.50%
9.20%
Quarterly
10%
4
2.50%
10.38%
Monthly
8.5%
12
0.71%
8.84%
Daily
3.25%
365
0.01%
3.30%

Question 2: Periodic Interest Rate
Given:
This is a Saving Account, no adding or withdrawing from the account
Which is favorable?
Daily compound rate of 0.045%
Weekly compounded rate of 0.285%
Monthly compounded rate of 1.15%
Quarterly compounded rate of 4.325%
Semiannual compounded rate of 8.5%
(i) An interest rate compounded annually is favorable, since it yields the highest Effective Annual Rate of Interest, and will accumulate more interest after the given period.

Period
Annual percentage rate (APR)
Compounding per Year
Periodic rate
Periodic Interest Rate (P)
Effective Annual Rate
(i)
Annually
16%
1
16%
16%
Semiannually
8.5%
2
4.25%
8.68%
Quarterly
4.25%
4
1.06%
4.32%
Monthly
1.15%
12
0.10%
1.16%
Weekly
0.285%
48
0.01%
0.29%
Daily
0.045%
365
0.00%
0.05%

(ii) Therefore Effective Annual Rate (in 2 decimal places) = 0.05%

Period
Annual percentage rate (APR)
Compounding per Year
Periodic rate
Periodic Interest Rate (P)
Effective Annual Rate
(i)
Daily
0.045%
365
0.00012%
0.045%

Question 3: EAR

Period
Annual percentage rate (APR)
Compounding per Year

References: Fouque, J., & Papanicolaou, G. (2011). Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives. Cambridge: Cambridge University Press.