# 18123 - 8.4#2 The future value of the installment plan 3...

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Unformatted text preview: 8.4, #2. The future value of the installment plan 3 years from now when the final payment is made is 5000 + 5000e0.08 + 5000e2(0.08) + 5000e3(0.08) = 22640.24 The future value of \$25000 paid 3 years from now is \$25000. Thus the lump payment is preferable. Alternatively, one can calculate the present values of the two options to see the lump payment is preferable. 8.4, #3. The present value of the income stream is 15 0 3000e-0.06t dt = 3000 e-0.06t -0.06 = 29671.52. 15 0 The future value of the income stream is 15 15 3000e0.06(15-t) dt = 3000e0.9 0 0 e-0.06t dt e-0.06t -0.06 15 0 = 3000e 0.9 = 72980.16 8.4, #5. If P dollars is deposited at a continuous each year into the account, the future value of the stream in 10 years time is 10 10 Pe 0 0.1(10-t) dt = P e 0 e-0.1t dt = -P e e-0.1t 0.1 10 0 = 10P e(1 - e-1 ). This is \$100000 if P = 10000/(e - 1) = 5819.77. The future value at the end of 10 years of a lump sum of L dollars deposited now is Le(0.1)10 = Le. This is \$100000 if L = 100000/e = 36787.94. 8.4, #7. In (a) the future value of the deposit stream at time T is T 0 1000e0.05(T -t) dt = -20000e0.05(T -t) T 0 = 20000(e0.05T - 1). 20000(e0.05T - 1) = 10000 when e0.05T = 1.5, that is , when 0.05T = ln 1.5 and T = 8.11 years. In (b) the future value of the deposit stream at time T is 2000e0.05T + 20000(e0.05T - 1) = 22000e0.05T - 20000. 22000e0.05T - 20000 = 10000 when e0.05 = 32/22 = 1.3636, that is, when 0.05T = 0.3102 and T = 6.20 years. ...
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