# Use simple and compound interest to find the ending balance 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. 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.

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