Question #233736

Situation 1

b) If $100 at Time “0” will be worth $110 a year later and was $90 a year ago, compute the interest rate for the past year and the interest rate next year.

c) Assume that $90 invested a year ago will return $110 a year from now. What is the annual interest rate in this situation?

b) If $100 at Time “0” will be worth $110 a year later and was $90 a year ago, compute the interest rate for the past year and the interest rate next year.

c) Assume that $90 invested a year ago will return $110 a year from now. What is the annual interest rate in this situation?

Expert's answer

(b)

• Taking the case from 90$ to 100$ in a year

rate of interest"(R)=(\\frac{(A-P)}{P})\\times100=(\\frac{(100-90)}{90}) \\times100 =11.11\\%" per anum (annually),where A=amount and P= principal

• Taking the next case from 100$ to 110$ in a year

rate of interest"(R)=(\\frac{(A-P)}{P})\\times100=10\\%" per anum (annually)

(c)

• Investment was made a year ago and return was obtained a year from now so it means 2 successive years

.i.e. T=2 years

• Assuming it to be compounded annually from 90$ to 110$

"A=P(1+\\frac{R}{100} \\times n )^{nT}" ,where n=no of times it is compounded annually, t= no of years

"110=90(1+\\frac{R}{100})2" , because "n=1" "(\\frac{110}{90})(1\/2)=1+\\frac{R}{100}"

"R=((\\frac{110}{90})1\/2-1)\\times100=10.55\\%"

• Assuming it to be simple interest

"I=P\\times R \\times T"

"20=\\frac{(90\\times R \\times2)}{100}"

"R=\\frac{(20\\times100)}{2\\times90}=11.11\\%"

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