This preview shows page 1. Sign up to view the full content.
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 3000e0.06t dt = 3000 e0.06t 0.06 = 29671.52. 15 0 The future value of the income stream is
15 15 3000e0.06(15t) dt = 3000e0.9
0 0 e0.06t dt e0.06t 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(10t) dt = P e
0 e0.1t dt = P e e0.1t 0.1 10 0 = 10P e(1  e1 ). 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. ...
View
Full
Document
This note was uploaded on 07/06/2011 for the course MATH 180 taught by Professor Tan during the Fall '08 term at Ill. Chicago.
 Fall '08
 TAN
 Calculus

Click to edit the document details