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A building society add interest monthly to investors accounts even though interest rates are expressed in annual terms. The current rate of interest is 6% per year.
An investor deposits $1000 on 1 January. How much interest will have been earned by 30th June?
Sir i have watched your free lectures?still i am not able to do this question.
The formula i know is
Px(1+r)n Or
And 1+R=(1+r)12
But the answer is
Current rate is 6%pa payable monthly
Effective rate is 6/12%=1/2% compound every month
In the six months from January to June, interest earned=
($1000x(1.005)6 – $1000= $30.38
Sir I cant use the two formula above??i dont get it?? Please helpBecause they are adding interest monthly, and because there are 12 months in a year, the interest added each month is 6%/12 = 0.5% (or 0.005)
Using the formula ( P x (1+r)^n) gives that the amount in 6 months time will be:
1,000 x (1/005)^6 = $1,030.38. the extra $30.38 is the interest earned.
Alternatively, using the formula 1+R = (1+r)^n gives that the 6 month interest rate is:
R = (1.005^6) – 1 = 0.03038 (or 3.038%)
So the interest earned in 6 months is 0.03038 x $1,000 = $30.38
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