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Question

A man borrows Rs. 20,000 at 12% per annum, compounded semi-annually and agrees to pay it in 10 equal semi-annual installments. Find the value of each installment, if the first payment is due at the end of two years.

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Solution

This is a case of deferred annuity. The segment depicts 10 semi-annuals of 5 years. The first installment is paid at the end of two years.
Let the value of each instalment be a.
The formula for deferred annuity is
P=ai.(1+i)n1(1+i)m+n
Here, m=3,n=7 m+n=10,P=Rs.20,000
12100×12=0.06
20,000=a0.06.(1+0.06)71(1+0.06)10
20,000=a0.06.(1.06)71(1+0.06)10
20,000=a0.06.1.50311.791
20,000=a0.06×0.5031.791
a=20,000×0.06×1.7910.503
a=2149.20.503
a=427.76
Hence, each instalment is of Rs. 427.67
624747_596059_ans_278983b61cb44b1ea0a49d9ecee3834b.png

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