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Hi Sir
I watched your lecture on this chapter and have a question
If $1,000 is invested for three years at a 4% six monthly interest rate.
At the end of the three years,what will be the worth of invt ?This is my answer
4% six month rate = there are two 6 months in an year
Therefore “n” will be 2 time * 3 years = 6 times compounding over the period1000 * ( 1.04)^6 = 1265.31
So in this question how will we find the Effective annual rate ?
I was trying to work it out like you demonstrated.The interest we paid in total was 1265.31 – 1000 = 265.31 / 1000 = 26 %
Is this right ?
No, that is not right. 26.53% is the three year interest rate.
To get the effective annual rate, then since there are two 6 months in a year it is 1.04^2 -1 = 0.0816 or 8.16%.
(Also, it checks nicely, because 1,000 invested for 3 years at 8.16% per year will grow to
1,000 x 1.0816^3 = 1,265.31 🙂 )Hello sir!!!!
Could you please tell me how the answer is 12.554$ and explain also this question.What will be the amount of sum of an investment made 3 years back of amount 4,000$ with 10% interest compounded quarterly ?
Ans: 12,554$There are 12 quarters in 3 years.
If interest of 10% is added every quarter, then at the end of 3 years the amount will have grown to 4,000 x (1.10^12) = 12,554
Have you watched my free lectures on interest?
Because the question does not ask for it! By all means calculate the effective annual rate and then use that, but it takes longer and is not necessary.
Again, have you watched my free lectures on interest?
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