Math Question: Ben deposited $1,200 in a certificate of deposit (CD) at an interest rate of 5.5%. He earned $198 in simple interest. How long was his money invested in the CD?Immersive Reader

Assuming 5.5% is an annual percentage rate: Use the formula A=P(1+rt) where A = final amount P = initial principal balance r = annual interest rate t = time (in years) P is $1200, and A is $1200+$198=$1398 (Ben still owns his initial principal back in additional to his earnings). r is the rate, which is the percentage 5.5% but divided by 100: 5.5% equals 0.055, or 5.5 percent equals 5 and 1/2 hundredths or 55 thousandths (all the same, like 1000 meters is 1 kilometer). t is our unknown, the length of time which the money has been getting interest in the CD. A=$1398 P=$1200 r=0.055 t=? Use the formula A=P(1+rt). It has 4 "unknowns" but we know three of them, so we can solve for the fourth: A=P(1+rt) $1398=P(1+rt) $1398=$1200(1+rt) $1398=$1200(1+0.055t) now we just solve for t. $1398=$1200(1+0.055t) divide by $1200: ($1398)/($1200)=($1200)/($1200)(1+0.055t) ($1398)/($1200)=(1+0.055t) ($1398)/($1200)=1+0.055t subtract 1 from each side: ($1398)/($1200)-1=1-1+0.055t ($1398)/($1200)-1=0.055t divide by 0.055: ($1398)/($1200)-1=0.055t ($1398)/($1200)-1=(0.055)t [($1398)/($1200)-1]/(0.055)=(0.055)/(0.055)t [($1398)/($1200)-1]/(0.055)=(1)t [($1398)/($1200)-1]/(0.055)=t we've isolated t at this point, but we still need to simplify: $1398/$1200=1.165 (the dollars cancel as well) [($1398)/($1200)-1]/(0.055)=t (1.165-1)/0.055=t 0.165/0.055=t 3=t t=3 to check I just plugged this: 1200(1+3*0.055)-1200 into the google search bar, and it gave me 198. So Ben's money was in the CD for 3 years. (Again, assuming 5.5% is an APR or annual percentage rate; if a different problem specifies monthly or daily or whatever, go with what that problem says).
Answered On 05/27/2020 12:11