Question
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Rust Bucket Motor Credit Corporation (RBMCC), a subsidiary of Rust Bucket Motor, offered some securities for sale to the public on March 28, 2008. Under the terms of the deal. RBMCC promised to repay the owner of one of these securities $100,000 on March 28. 2039, but investors would receive nothing until then. Investors paid RBMCC $23.699 for each of these securities: so they gave up $23.699 on March 28. 2008. for the promise of a $100,000 payment 31 years later Based on the $23,699 price, what rate was RBMCC paying to borrow money? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16)) Rate of return % Suppose that, on March 28, 2018, this security's price is $41,980 If an investor had purchased it for $23,699 at the offering and sold it on this day, what annual rate of return would she have earned? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16)) Annual rate of return % If an investor had purchased the security at market on March 28. 2018. and held it until it matured, what annual rate of return would she have earned? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g.. 32.16)) Annual rate of return % At 6 30 percent interest, how long does it take to double your money? (Round your answer to 2 decimal places, (e.g., 32.16)) Length of time years At 6 30 percent interest, how long does it take to quadruple it? (Round your answer to 2 decimal places, (e.g., 32.16)) Length of time years You are scheduled to receive $11.500 in four years. When you receive it, you will invest it for five more years at 6.4 percent per year. How much will you have in nine years? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16)) Future value $
Explanation / Answer
We have Maturity value = FV = 100,000
Prseent value = PV = 23699
nper = 31 Yrs
So Rate = Rate(nper,pmt,pv,fv)
= Rate(31,0,-23699,100000)
= 4.75% ,...............Ans (a)
We have Sale value = FV = 41960
Prseent value = PV = 23699
nper = 10 Yrs
So Rate = Rate(nper,pmt,pv,fv)
= Rate(10,0,-23699,41960)
= 5.88% .............>>>Ans (b)
We have Mkt value in 2018 = FV = Fv(rate,nper,pmt,PV)
= FV(4.75%,10,0,23699)
= $37,693.84
So This value become purchase price in 2018 for investor
So PV = $37,693.84
Maturyiy in 2039 ie after 2039-2018 = 21 yrs = nper
Maturity value = FV = 100,000
So Rate = Rate(nper,pmt,pv,fv)
= Rate(21,0,-37693.84,100000)
= 4.76% ...............>>Ans (c)
We have PV = x & FV = 2x, Rate i = 6.3%
We have FV = PV*(1+i)^n
So (1+i)^n = FV/PV = 2x/x = 2
SO (1+6.3%)^n = 2
ie n Log(1+6.3%) = Log 2
So n = Log(2)/Log(1.063) = 11.35 Yrs
So No of yrs reqd = 11.35 Yrs ...............Ans
We have PV = x & FV = 4x, Rate i = 6.3%
We have FV = PV*(1+i)^n
So (1+i)^n = FV/PV = 4x/x = 4
SO (1+6.3%)^n = 4
ie n Log(1+6.3%) = Log 4
So n = Log(4)/Log(1.063) = 22.69Yrs
So No of yrs reqd = 22.69 Yrs ............>Ans
We hve PV = 11500, n = 5, i = 6.4%
So AFter 9 yrs, you have FV = PV*(1+i)^n
= 11500*(1+6.4%)^5
= $15,682.16 ..................>>Ans