Apply the Future-Value equation: F = P(1 + i)^{n}

where F = Future Value, P = Present Value, i = Interest Rate, n = number of compounding periods

F = 2000

P = 1972.81

n = 14 weeks / 52 (weeks / year) = 0.26923 year

Equation Rearrangement 1:

P(1 + i)^{n} = F

Equation Rearrangement 2:

(1 + i)^{n} = F / P

Equation Values Assignment:

(1 + i)^{0.26923} = 2000 / 1972.81

Apply logarithms:

Log[(1 + i)^{0.26923}] = Log[1.013782] = 0.005945

0.26923 * Log[(1 + i)] = 0.005945 Power property of logarithms: Log[a^{n}] = n * Log[a]

Log[(1 + i)] = 0.005945 / 0.26923 = 0.0220804

1 + i = 10^{0.0220804}

Reduce to the solution:

i = 10^{0.0220804} - 1 = 1.05216 - 1

i = 0.05216

i = 0.05216 * 100% = 5.216% equivalent annual rate of return (ANS)

Check the solution:

$1972.81 * (1 + 0.05216)^{14/52 year} = $2000.00 (OKAY)

I hope this helps you,

Gary