Hi John, A bank adds interest monthly to investors' accounts even though interest rates are expressed in annual terms. The current rate of interest is 12%. Fred deposits $2000 on 1 July.
How much interest will have been earned by 31 December (to the nearest $)?
A. $123
B. $60
C. $240
D. $120
I understand how they got the answer of $123.
But when i tried my own method of finding the effective annual rate first which i found by using the formula: R= (1 + r)^n -1.
I did: (1 + 0.01)^12 - 1 which i found to be 12.68%.
When i do 12.68%×2000 i get annual interest of $253 which when i divide by 2 to reflect the 6 month period i get $126.80 not the $123 which is the answer.
Please help me, where am i going wrong? Is my method not correct?
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Effective interest rate
9y ago#1The interest per month is 12%/12 = 1% per month
2,000 invested now for 6 months (from July to December) will grow to 2,000 x 1.01^6 which equals 2,123
So the interest earned is 2,123 - 2,000 = 123
Your method is not correct because just as you correctly understand that 1% per month does not man the effective rate is simply 1% x 12, you cannot say that the six monthly rate is simply the yearly rate divided by 2.
Since the annual rate is 12.68%, the rate for 6 months is given by (1+r)^2 = 1.1268
So the six monthly rate = r = (sq root of 1.1268) - 1 = 0.0615 or 6.15%
Therefore 2,000 for six months will have grown to 2,000 x 1.0615 = 2,123
So the same answer as above :-)
Oh i see... thankyou very much John. It is crystal clear now.
9y ago#3You are welcome :-)
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