Question

What is the size of the payments that must be deposited at the beginning of each 6-month period in an account that pays 9.4%, compounded semiannually, so that the account will have a future value of $160,000 at the end of 18 years? (Round your answer to the nearest cent.)

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I'm all set on this one. thanks, it is 7051.77

Answer 1

Payments are made at the beginning of each period, that means at the end of previous period. We can find the Payment for each period using trial and error method and disocunts it at 4.70% semi annually for 36 semi annuals. Present Value S 8,883 8,484 Computation of Cashflow equals to $ 160,000/. :- Semi Cash PVF Payment Annual flows S @4.70% 8,882.50 1.0000 8,882.50 0.9551 8,882.50 0.9122 8,882.50 0.8713 8,882.50 0.8322 8,882.50 0.7948 8,882.50 0.7591 8,882.50 0.7251 8,882.50 0.6925 8,882.50 0.6614 8,882.50 0.6317 8,882.50 0.6034 8,882.50 0.5763 8,882.50 0.5504 8,882.50 0.5257 8,882.50 0.5021 8,882.50 0.4796 8,882.50 0.4580 8,882.50 0.4375 8,882.50 0.4178 8,882.50 0.3991 8,882.50 0.3812 8,882.50 0.3641 8,882.50 0.3477 8,882.50 0.3321 8,882.50 0.3172 8,882.50 0.3030 8,882.50 0.2894 8,882.50 0.2764 8,882.50 0.2640 8,882.50 0.2521 8,882.50 0.2408 8,882.50 0.2300 8,882.50 0.2197 8,882.50 0.2098 8,882.50 0.2004 Present Value 8,103 7,739 7,392 7,060 6,743 6,440 6,151 5,875 5,611 5,359 5,119 4,889 4,670 4,460 4,260 4,069 3,886 3,711 3,545 3,386 3,234 3,089 2,950 2,818 2,691 2,570 2,455 2,345 2,239 2,139 2,043 1,951 1,864 1,780 160,001 Answer is $ 8,882.50/.