A principal amount P, at the rate of interest r per annum, after a time period t years increases to `P_f = P + P*t*r`
Compound interest refers to the situation where interest in any period is earned by both the principal and the interest earned in all the periods. A principal amount P, at the rate of interest r per annum, after a time period t years increases to `P_f = P(1+r)^t`
In the problem, the principal P = $7,900, and the rate of interest is 16%. The simple interest earned on this in a year is equal to $1,264. The ending balance is equal to $9,164.
As in the case of compound interest, compounding is done weekly; the effective interest rate is 0.16/52, and the time period is 52 weeks.
The final balance in this case is `7,900*(1+.16/52)^52` = 7,900*1.17322=9,268.45.
For a principal of $7,900 at 16% compounded weekly for one year, the ending balance after a year is $9,164 if simple interest is earned, and it is $9,268.45 if compound interest is earned.