At the end of each three months Laura puts $200 into anaccount which pays 10% co
ID: 2662299 • Letter: A
Question
At the end of each three months Laura puts $200 into anaccount which pays 10% compounded quarterly. After 10 yearsshe discontinues the payments but leaves the total amount in theaccount to collect interest for 2 more years. Determine the balancein the account at the end of 12 years. Do I strart this by setting up a geometric sequence for the1st 10 years of the accound and then do the compounded interest onthe result for the last two year? I need to see how thiswould be worked out - Will rate a lifesaver! At the end of each three months Laura puts $200 into anaccount which pays 10% compounded quarterly. After 10 yearsshe discontinues the payments but leaves the total amount in theaccount to collect interest for 2 more years. Determine the balancein the account at the end of 12 years. Do I strart this by setting up a geometric sequence for the1st 10 years of the accound and then do the compounded interest onthe result for the last two year? I need to see how thiswould be worked out - Will rate a lifesaver!Explanation / Answer
This Solution has 2 parts. First calculate FV of annuity of 10 Yrs of $200 per Qtr @10%. Then Calculate FV of the deposit (equal to FV of annuity) for 2 yrs@10%. For annuity case here... N=10 Yrs, K=Int rate = 10%, PMT =$200. m= 4 periods (Qtryly Interest) FV of annuity = PMT*[(1+K/m)^(m*N)-1]/(K/m) So FV of annuity = 200*[(1+10%/4)^(4*10) -1]/(10%/4) ie FV = 200*[1.025^40 -1]/0.025 = 200*(2.6851-1)/0.025 =13480.51 So at end of 10Yrs, Laura will have$13,480.51. Now This money will stay invested for 2 yrs @10% Qtrlycompounding. So at end of 2 yrs, The amount is given by FV = PV (1+i/m)^(m*n) where i=10%, m=4 ie qteryly compounding &PV = $13,480.51, n=2yrs So FV = 13480.51*(1+10%/4)^(4*2) = 13480.51*(1.025)^8 =13480.51*1.2184 = $16,424.65 So Laura will have $16,424.65 at end of 10Yrs+2Yrs.
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