Question

Randall has an account balance of $675.54 in a savings account that earns interest at a rate of 2.5% compounded twice a year. If Randall opened the account eleven years ago, what was the principal deposit rounded to the nearest dollar?
ALSO

Agatha has deposited $541 in a savings account that earns interest at a rate of 2.4% compounded twice a year. What will the account balance be in 17 years?

Answer 1

To calculate amount accrued after a given period of time we use the compound interest formula: A= P(1+r/100)∧n where A i the amount, P is the principal amount, r is the rate of interest and n is the interest period.
In the first part; A= $ 675.54, r= 1.25% (compounded semi-annually) and n =22 ( 11 years ),  hence, 675.54 = P( 1.0125)∧22
   = 675.54= 1.314P
 P= $ 514.109 , therefore the principal amount was $ 514 (to nearest dollar)
Part 2
principal amount (p)= $ 541, rate (r) = 1.2 % (compounded twice a year thus rate for one half will be 2.4/2) and the interest period (n)= 34 (17 years×2)
Amount= 541 (1.012)∧34
             = 541 ×1.5
             = $ 811.5
Therefore, the account balance after $ 811.5.