ASSIST WITH ALGERBRA WORD PROBLEMS

Question

THE FUTURE VALUE OF A SIMPLE INTEREST INVESTMENT GIVEN BY s=p(1+RT)WHERE P IS THE PRINCIPAL INTEREST RATE R FOR T YEARS.  WHAT PRICNIPAL P MUST BE INVESTED FOR T-10 MONTHS AT THE SIMPLE INTEREST RATE R=5% SO THAT THE FUTURE VALUSE GROWS TO $2500

Answer 1

We want s to be $2500, R = 5%, and T = 10 months.  In the formula s = p(1 + RT), T must be in years, so we have to convert our T into years:  T = 10 months = 0.833 years.

 

We know p = s/(1 + RT)

In our case that is 2500/(1 + (0.05)(0.833)) = 2500/(1.041666) = 2400

Answer 2

s=p(1+RT),  ................ (1)   WHERE p IS THE PRINCIPAL, INTEREST RATE is R, and T is term of deposit in YEARS

For calcualting interest earned in T= 10 MONTHS, 10 minths need to be converted into years to fit in the given relationship (1).. thus 12 months = 1year

          =>1 month =1/12 year  by rule of proportions

         =>10 month = 10/12 year

                            =5/6 year

from (1) we have

2500=p(1+[5/100][5/6])) , where s=$2500, R=5%=5/100, T=5/6 years

=>2500=p[1+ 5 * 5 /( 100 ₄*6)] ........ simplifying

=>2500=p[1+1/24] ....................simplifying

=>2500=p*25/24

=>p= ¹⁰⁰ 2500 *24/ 25 .... dividing both by 24/25

=>p=2400

 

Hence the $2400 must be invested for 10 month at the simple interest rate of 5% so that the future value grows to $2500.