# Answer to Question #233736 in Civil and Environmental Engineering for Alan Enrico V Tuib

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 $110 a year from now. What is the annual interest rate in this situation? 1 Expert's answer 2021-09-10T00:03:49-0400 ﻿(b) • Taking the case from 90$ 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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