A bank is offering following choices to a customer for interest on fixed deposits. Which will be the most beneficial to the customer ?
10% per annum compounded yearly
The nominal rates differ and so do the compounding frequencies, so the four offers cannot be compared directly. Convert each to its effective annual rate using \(\left(1 + \frac{r}{n}\right)^{n} - 1\), where \(r\) is the nominal annual rate and \(n\) the number of compoundings in a year.
10% compounded yearly: \(n = 1\), so the effective rate is simply 10%.
9% compounded six monthly: \((1.045)^{2} - 1 = 1.092025 - 1 = 0.092025\), that is 9.20%.
8% compounded quarterly: \((1.02)^{4} - 1 = 1.08243 - 1 = 0.08243\), that is 8.24%.
7% compounded monthly: \(\left(1 + \frac{0.07}{12}\right)^{12} - 1 = 0.0723\), that is 7.23%.
More frequent compounding does raise the effective rate above the nominal one, but here the gap between the nominal rates is far wider than any gain from frequency — the largest such gain is only about 0.20 of a percentage point, while the rates themselves are spread over three points.
Hence the most beneficial choice is 10% per annum compounded yearly.
Similar Questions
How long would it take to double the amount deposited in a fixed income security carrying 12% rate of interest ?
Important Questions from Compound Interest
A person borrowed Rs. 10000 on compound interest at the rate of 40 percent per annum. If the interest is compounded half yearly, then what will be the amount to be paid after 1.5 years?
In how many years will a sum of Rs.1875 amount to Rs.2187 at 8 percent p.a. compound interest?
A sum of money has increased by 45% in 9 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
At a certain rate of compound interest a certain sum amounts to Rs. 64800 in 4 years and Rs. 93312 in 6 years. What is the compound interest earned in fifth year?
Karuna has an option to invest in the following three schemes. If she wants to invest Rs P, then which scheme will be most beneficial for her?
Scheme that comes with lower interest rates and terms;
I. 28% p.a. interest, compounded every quarter, for one year.
II. 28% p.a. interest, compounded every half year, for one year.
III. 28% p.a. interest, for one year, compounded every year.
