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Question
A bank pays 8% per annum interest compounded quarterly. Find the equal deposits to be made at the end of each quarter for 10 years to have ₹ 30,200? [(1.02)40 = 2.2080]
Solution
Here A = ₹ 30200, i = `8/100`
`"i"/"k" = (8/100)/4 = 2/100` = 0.02, n = 10, k = 4
A = `"a"/("i"/"k") [(1 + "i"/"k")^("nk") - 1]`
30200 = `"a"/0.02 [(1 + 0.02)^40 - 1]`
30200 = `("a" xx 100)/2 [(1.02)^40 - 1]`
30200 = `("a" xx 100)/2 [2.2080 - 1]`
`(30200 xx 2)/100` = a[1.2080]
302 × 2 = a[1.2080]
a = `(302 xx 2)/1.2080`
= ₹ 500
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