On January 1 , 1980 , Jack deposited $ 1 , 000 into bank X to earn interest at a nominal annual rate of j compounded semiannually. On January 1 , 1985 , he transferred his account to bank Y to earn interest at a nominal annual rate of k compounded quarterly. On January 1 , 1988 , the balance at bank Y is $ 1 , 990.76 . If Jack could have earned interest at nominal annual rate of k compounded quarterly from January 1 , 1980 through January 1 , 1988 , his balance would have been $ 2 , 203.76 . Calculate the ratio of k to j .

1.25

Explanation:

1000*(1+x)^8 = 2203.76

(1+x)^8 = 2203.76/1000

(1+x)^8 = 2.20376

Taking root of both side

(1+x)^8^(1/8) = 2.20376^(1/8)

1 + x = 1.10381308235

x = 1.10381308235 - 1

x = 0.10381308235

x = 10.38%(Equ 1)

1000*((1+y)^5)*((1+x)^3) = 1990.76

1000*((1+y)^5)*1.344889 = 1990.76

((1+y)^5) = 1.48024

Taking root of both side

((1+y)^5)^(1/5) = 1.48024^(1/5)

1+y = 1.08159937381

y = 1.08159937381 - 1

y = 0.08159937381

y = 18.15995%(Equ ii)

J = (((1+y)^1/2)-1)*2

J = (((1+0.08159937381)^1/2) - 1)*2

J = (1.039999698947072 - 1)*2

J = .039999698947072 * 2

J = 0.079999397894144

J = 7.9999%

J = 8%

K = (((1+x)^1/4)-1)*4

K = (((1+0.10381308235 )^1/4)-1)*4

K = 10%

So K/J = 10/8 = 1.25