Provide an appropriate response 1) An interest rate of 8% compounded semiannuall

Question

Provide an appropriate response 1) An interest rate of 8% compounded semiannually corresponds to an effective rate of A) 8.1600%. B) 9.2456%. C) 12%. D) 8%. E) 8.2031% 2) A trust fund is to be established by a single payment so that at the end of 15 years, there will be$20,000 in the fund. If the fund earns interest at the rate of 8% compounded semiannually, how much should be deposited initially into the fund? A) $6166.38 B) 86472.42 C) $7143.56 D) 811,105.30 E) $7014.27 3) A debt of 3 2000 due in one year is to be repaid by a payment due two years from now and a final payment of $1000 three years from now. If the interest is at the rate of 4% compounded annually, then the payment due in two years is A) $1155.43. B) $1203.14 c)I 1118.46 D) 81191.00 E) 1000.00 4) If an investment 013 20,000 earns interest at an annual rate of 9% compounded continuously, then the value (in dollars) of the investment six years from now is A) 20,000(1.09)-6 B) 20,000(1.09)6 C) 20,000e0.54 D) 20,000e-0.54 0.54 20,000 E) 5) If an investment of $12,000 earns interest at an annual rate of 7% compounded continuously, then the value (in dollars) of the investment ten years from now is A) 12000(1.07)10 B) 12,000(1.07)-10 12,000 D) 12,000e0.7 E) 12,000-0.7 6) If money earns interest at an annual rate of 8% compounded continuously, then the value (in dollars) of $10.000 due at the end of five years is A) 10,000e0.4 B) 10,000 C) 10,000e0.4 D) 10,000(1.08)-5 E) 10,000(1.08)5

Explanation / Answer

1)effective interest rate =(1 +r/n)n-1

r =rate of interest =8%=0.08, n =number of times compounded in an year =2

effective interest rate =(1 + 0.08/2)2-1

effective interest rate =0.0816

effective interest rate =8.1600%

2)A=P(1+ r/n)nt

A=amount after t year =20000

P =amount needed initially

t =number of years=15

n =number of times compounded in year =2

r=rate of interest =8%=0.08

20000=P(1+ 0.08/2)2*15

20000=P(1.04)30

P=20000/(1.04)30

P=6166.38$

6166.38$ should be deposited initially

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