Compound Interest
posted by Math .
A bank offers a rate of 5.3% compounded semiannually on its four year GICs(Guaranteed Investment Certificates). What monthly and annually compounded rates should it quote in order to have the same effective interest rate at all three nominal rates?

for the rate compounded monthly equivalent to a rate of 5.3% compounded semiannually :
let the monthly rate be i
then
(1+i)^12 = (1 + .053/2)^2 , take √
(1+i)^6 = 1.0265 , now take the 6th root
1+i = 1.004368675
so i = .004368675
so the annual rate is 12(.004368675)
= .052424
So 5.2424% compounded monthly is equal to 5.3% compounded semiannually
for the annual rate,
let the annual rate be j
(1+j) = (1 + .053/2)2
1+j = 1.053702
j = .053702 > an annual rate of 5.3702% 
if grandpa payed an insurance policy weekly payments of $1.02 at 3 and 1/2 percent interest compounded annually for 49 years(588 months) how much would it payout after his death to granddaughter? Based on Commissions 1961 Standard Industrial Mortality Table.
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