Question

5. How long will it take money to double if it is invested at (A) 8% compounded semiannually? (B) 7% compounded semiannually? 6. Bank A offers a 2-year GIC that pays 4.82% compounded continuously and Bank B offers a 2-year GIC that pays 4.85% compounded quarterly. Find the annual percentage yield (or effective rate) for each one Which bank's GIC has the higher return?

Answer 1

Solution 2 (4) less principal - a and amount = an ra 8% = 8 = tinue a 4 x 2 = 2t 4% semiannually semiannual any z wy ( 14 ) 22 (loogget taking Cof both fieles. Tone I at top (1004) | 00.3010 2 2000 0170) 2t = It a tz 0.3010 000170 17.706 i 8.85 year.! (3) и т. п. = 1 2 3Г./* {e @милеу 2 A = P( it rit
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PAGE No Kl+35) g. (1.035 lat taking log both pibles , we get lag a at lop 1.035 0.3010 = at x 0.0149 0-30/0 & 0.0298 t + 2 I(A)=8 % (B) = 7.1. 03010 z 10-40728 0-0298 = d.85 yeans ! 2 10.10 years 6 a Effective rate of Return a Pent / Amount at compounded continously : suppose pal 824.82% t=2Yo.. Az Poe 82 A arxent A 2 0.0964 taking log both sides lop Aa 0-0964 loge logy (0.4343) (0.0964). Az Antily (00187)

effective Rate / 6 A = l.lol Interest & A-P = 16101- 1 = 1.101-1² 0-101 effective rate of return = 10.1% Effective Rate of lethen when compounded quasedy! = (1+r) - 1 here, & = 4.85% = 0.0485 / 4 = 0·0/2125 = n = 4 elto x 2 % 2 80tr. pretting the values in fonul, we get = (1+0.010125) -/ = (1.012125102 - het we (1•012125) º taking log both sides for a 8 g (1.0/2/25) log na 0.0408 x= Autiles (0.0408) d - 6099 By putting this reclue in cå we get = 1.099 = 4099 = 9.9% Effective Rate fortune of comppuudley continuously is higher je 16.1%