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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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)n−1(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)7−1(1+0.06)10 20,000=a0.06.(1.06)7−1(1+0.06)10 20,000=a0.06.1.503−11.791 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