Question

I don’t understand theses, te equation itself would help a lot ten an explanation

Answer 1

Simple interest is always computed on the original principal amount. The interest for every time period is the same. The formula
.. I = P*r*t
is used to compute the interest (I) on the principal amount (P) for a given rate (r) and time period (t).

5) On Olivia's account, the interest at the end of 3 years will be
.. I = Prt
.. I = 1530*0.06*3 . . . . . interest is "per year" and time is in years.
.. I = 275.40
This amount of interest is added to Olivia's account to give a balance of
.. balance = principal + interest
.. = 1530 +275.40 = 1805.40

When interest is compounded, it is computed not on the original principal amount (except in the first period), but on the account balance at the beginning of the period. That account balance will include any interest earned up to that point. For a given principal amount (P) and periodic interest rate (r), the account balance at the end of t periods of time will be
.. balance = P*(1 +r)^t
Here, interest is compounded annually, so "r" is the annual rate and "t" is the number of years. At the end of 3 years, Melinda's account balance will be
.. balance = 1500*(1 +.08)^3
.. = 1889.57

Melinda's account has 1889.57 -1805.40 = 84.17 more than Olivia's account. This corresponds to selection D.


6) Account 1 will have a balance after 2 years of
.. balance = principal +interest = P +P*r*t = P*(1 +r*t)
.. = 400*(1 +.035*2) = 428

Account 2 will have a balance after 2 years of
.. balance = P*(1 +r)^t
.. = 250*(1 +.0325)^2 = 266.51

The total of the two accounts will be 428 +266.51 = 694.51. This corresponds to selection J.