Question

If you were given a choice of investing in an account that paid quarterly interest and one that paid monthly interest, which one should you choose if they both offer the same stated interest rate and why?

Answer 1

If an investment opportunity comes with same interest rate but with diifferent frequency of interest payments, better choice is to choose the one with the more frequent payment mainly in case if interest is compounded.

In case of compounding interest, the effective interest rate will increase as the frequency of interest payment is lesser.

For example, assume a investment of $100 at annual rate of interest of 10% for one year.

Value of investment if interest is compounded:

Month	Interest compounded monthly	Interest compounded quarterly
Beginning Balance	Interest (beginning balance * 10%/12)	Closing Balance	Beginning Balance	Interest (beginning balance * 10%/4)	Closing Balance
1	100.00	0.83	100.83	100.00		100.00
2	100.83	0.84	101.67	100.00		100.00
3	101.67	0.85	102.52	100.00	2.50	102.50
4	102.52	0.85	103.38	102.50		102.50
5	103.38	0.86	104.24	102.50		102.50
6	104.24	0.87	105.11	102.50	2.56	105.06
7	105.11	0.88	105.98	105.06		105.06
8	105.98	0.88	106.86	105.06		105.06
9	106.86	0.89	107.75	105.06	2.63	107.69
10	107.75	0.90	108.65	107.69		107.69
11	108.65	0.91	109.56	107.69		107.69
12	109.56	0.91	110.47	107.69	2.69	110.38

Thus, as can be seen, a $100 investment becomes $110.47 at the end of 1 year if interest is compounded monthly which is higher than $110.38 which is compounded quarterly. Thus, monthly compounding effective interest rate is 10.47%(110.47/100-1) which is higher than the quarterly componding effective interest rate at 10.38% (110.38/100-1).

Effective interest rate can be compouted using the equation (1+i/n)^n-1

In the given example, monthly compounding effective interest rate = ((1+10%/12)^12)-1 = 10.47% and monthly compounding effective interest rate = ((1+10%/4)^4)-1 = 10.38%

Thus, monthly interest option is better than quarterly interst option for an investment providing compounding interest.

In case of investment having simple interest, it will be indifferent if the interest is paid monthly or quarterly as the total interest amount will anyways remain the same. However, monthly investment in such cases too provides more liquidity (as it is given every month) and hence could be preferred over quarterly payments.