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ACTSC 231 quiz3-soln

# ACTSC 231 quiz3-soln - -akor i;i cfw_>.0oc)fiz v k ot f G w...

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1. (apt,) Find the present value of a 20-year annuity which pays \$500 at the end of each month in the first 4 years, \$2,000 at the end of each quarter in the following 6 years, and \$8,000 at the end of each two yeaxs in the last 10 years. Assume the annual effective interest rate is 7%. i;:", G;;;i;," -akor {>.0oc) ot ffiz v+k + wo AAi Vi;, vrl',* 1 - (t+ ?/)l J-=t++? J ,ut1 clal&rtw *+ii \ r _A ?v= 20,1 /,7,3+o? 1p7,nq,I84Qrc7) ' + e7, v{ +,zl6r) ( l,o v )*'' \

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2. (5pt.) Tom pays continuously at a rate of 1500 * 100t per year for 10 years so that after 10 years Tom can sta"rt receiving an annuity of \$K per month payable in advance for 5 vears.Assume the force of interest function is as follows: ^ Itl(\$*r) for0<,<10, "'-10.04 for f >10, where t denotes the time measured in years. (a) (3pt.) Find the value at the end of 10 years of all the payments by Tom. (b) (2pt.) Find K. h)-TnL 4.0 vilne \$ Tuw,,r5 Try*e is llo (ro " ttoc4) n(e /,+ , Jo \- r\.- t = l("" rco(tt,++) ffid"+ =" (!o 250 o l( Y 'i,( .noQ =:tl)ZAo- /\ trt t^ \ '"6:.I( fi' t,l)=r1? (!l'Qrr')-'ds ) (^#) = tuly [ [n( ry+s)/-,', ) --1,['", tS=+ ( 3\( h Jt- l,n (rc++))=e'1t )+ -; - rr+t t-.f._r,..-,-,-- b).
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ACTSC 231 quiz3-soln - -akor i;i cfw_>.0oc)fiz v k ot f G w...

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