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CHAPTER 6 B-85 If the payments are an annuity due, the present value will be: PVA due = (1 + r ) PVA PVA due = (1 + .11)\$36,958.97 PVA due = \$41,024.46 b. We can find the future value of the ordinary annuity as: FVA = C {[(1 + r ) t – 1] / r } FVA = \$10,000{[(1 + .11) 5 – 1] / .11} FVA = \$62,278.01 If the payments are an annuity due, the future value will be: FVA due = (1 + r ) FVA FVA due = (1 + .11)\$62,278.01 FVA due = \$69,128.60 c. Assuming a positive interest rate, the present value of an annuity due will always be larger than the present value of an ordinary annuity. Each cash flow in an annuity due is received one period earlier, which means there is one period less to discount each cash flow. Assuming a positive interest rate, the future value of an ordinary due will always higher than the future value of an ordinary annuity. Since each cash flow is made one period sooner, each cash flow receives one extra period of compounding. 54. We need to use the PVA due equation, that is: PVA due = (1 + r) PVA Using this equation: PVA due = \$68,000 = [1 + (.0785/12)] × C [{1 – 1 / [1 + (.0785/12)] 60 } / (.0785/12) \$67,558.06 = \$ C {1 – [1 / (1 + .0785/12) 60 ]} / (.0785/12) C = \$1,364.99 Notice, when we find the payment for the PVA due, we simply discount the PV of the annuity due back one period. We then use this value as the PV of an ordinary annuity. 55. The payment for a loan repaid with equal payments is the annuity payment with the loan value as the PV of the annuity. So, the loan payment will be: PVA = \$42,000 = C {[1 – 1 / (1 + .08) 5 ] / .08} C = \$10,519.17 The interest payment is the beginning balance times the interest rate for the period, and the principal payment is the total payment minus the interest payment. The ending balance is the beginning balance minus the principal payment. The ending balance for a period is the beginning balance for the next period.

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