I need help in this question. Please I also posted the solution to same question with different values. Please use same method and solve both so i can get correct answers
1: To attract world-class post-docs, Kronos Labs wants to establish a research fund that will provide $50,000/year for 10 years beginning at some future date. Kronos has $100,000 now it can put immediately away at a 7.3% interest and can pay $10,000 per year into the fund starting next year for a to be determined number of years, say X. What minimum amount of time (to within one hundredth year like 9.78), X, does Kronos need to make payments before it can begin to offer the research fund to post-docs? I suggest you consider the cash flow diagram below: X Answer: Reasoning/Work 11.1 10 years 9-23: To attract world-class post-docs, Kronos Labs wants to establish a research fund that will provide $25,000/year for 15 years beginning at some future date. Kronos has $34,250 now it can put immediately away at a 9% interest and can pay $7,000 per year into the fund starting next year for a to be determined number of years, say X. What minimum number of years, X, does Kronos need to make payments before it can begin to offer the research fund to post-docs? I suggest you consider the cash flow diagram below: 1 PEF Answer: N = 10.60 years x Reasoning/Work: I've added some temporary cash flows (red arrows but not to scale) so as to construct a TVM equation that connects the various cash flows back to the present. One negative cash flow is 15 years already in the present which is the $34,250. The other negative cash flows are the yearly deposits of $7,000 and can be brought back to the present using the TVM equation P' = $7,000(P/A,9%,x). So the negative cash flows are: $34,250 + $7,000(P/A,9%,x) Which must be balanced by the positive cash flows of $25,000 yearly for 15 years starting after X years in the future. Now we can imagine a P" that is at X years that is the equivalent of those $25,000 cash flows, which would be given by P" = $25,000(P/A, 9%, 15) = $201,517.211. Now consider that P" is a future value relative to the present. To bring that future value, say F, back X years to the present, as say, P", We write: P""' = $201,517.211(P/F,9%,x) So now we can balance the positive and negative cash flows with this equation: $34,250 + $7,000(P/A,9%,X) = $201,517.211(P/F,9%,X) I used the TI-83 TVM Solver to find X by entering 1% = 9, N = 1 (initial guess), PV = -34250, PMT = -7000, and FV = 201517.21which gave N = 10.60 but also verified this by using the Excel NPER function: NPER(rate,pmt, pv, [fv], [type]) by entering rate = 0.09, pmt = -7000, pv = -34250, fv = 201517.21 which gave the same X as did the TI-83. O.COM es 1: To attract world-class post-docs, Kronos Labs wants to establish a research fund that will provide $50,000/year for 10 years beginning at some future date. Kronos has $100,000 now it can put immediately away at a 7.3% interest and can pay $10,000 per year into the fund starting next year for a to be determined number of years, say X. What minimum amount of time (to within one hundredth year like 9.78), X, does Kronos need to make payments before it can begin to offer the research fund to post-docs? I suggest you consider the cash flow diagram below: X Answer: Reasoning/Work 11.1 10 years 9-23: To attract world-class post-docs, Kronos Labs wants to establish a research fund that will provide $25,000/year for 15 years beginning at some future date. Kronos has $34,250 now it can put immediately away at a 9% interest and can pay $7,000 per year into the fund starting next year for a to be determined number of years, say X. What minimum number of years, X, does Kronos need to make payments before it can begin to offer the research fund to post-docs? I suggest you consider the cash flow diagram below: 1 PEF Answer: N = 10.60 years x Reasoning/Work: I've added some temporary cash flows (red arrows but not to scale) so as to construct a TVM equation that connects the various cash flows back to the present. One negative cash flow is 15 years already in the present which is the $34,250. The other negative cash flows are the yearly deposits of $7,000 and can be brought back to the present using the TVM equation P' = $7,000(P/A,9%,x). So the negative cash flows are: $34,250 + $7,000(P/A,9%,x) Which must be balanced by the positive cash flows of $25,000 yearly for 15 years starting after X years in the future. Now we can imagine a P" that is at X years that is the equivalent of those $25,000 cash flows, which would be given by P" = $25,000(P/A, 9%, 15) = $201,517.211. Now consider that P" is a future value relative to the present. To bring that future value, say F, back X years to the present, as say, P", We write: P""' = $201,517.211(P/F,9%,x) So now we can balance the positive and negative cash flows with this equation: $34,250 + $7,000(P/A,9%,X) = $201,517.211(P/F,9%,X) I used the TI-83 TVM Solver to find X by entering 1% = 9, N = 1 (initial guess), PV = -34250, PMT = -7000, and FV = 201517.21which gave N = 10.60 but also verified this by using the Excel NPER function: NPER(rate,pmt, pv, [fv], [type]) by entering rate = 0.09, pmt = -7000, pv = -34250, fv = 201517.21 which gave the same X as did the TI-83. O.COM es
