Question

# Gary decides to set up a retirement fund by depositing \$107 at the end of each...

Gary decides to set up a retirement fund by depositing \$107 at the end of each week for 22 years. How much will he have after 22 years, if the interest rate is 1.66%, compounded semiannually?

Annual interest rate = 1.66%
Semiannual interest rate = 0.83%

Effective annual rate = (1 + Semiannual interest rate)^2 - 1
Effective annual rate = (1 + 0.0083)^2 - 1
Effective annual rate = 1.0167 - 1
Effective annual rate = 0.0167 or 1.67%

Weekly interest rate = (1 + Effective annual rate)^(1/52) - 1
Weekly interest rate = (1 + 0.0167)^(1/52) - 1
Weekly interest rate = 1.00032 - 1
Weekly interest rate = 0.00032 or 0.032%

Weekly deposit = \$107
Period = 22 years or 1,144 weeks

Accumulated sum = \$107*1.00032^1,143 + \$107*1.00032^1,142 + …. + \$107*1.00032 + \$107
Accumulated sum = \$107 * (1.00032^1,144 - 1) / 0.00032
Accumulated sum = \$107 * 1,381.20674
Accumulated sum = \$147,789.12

So, he will have \$147,789.12 after 22 years.

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