Question

In an effort to save money for early retirement, an environmental engineering colleague plans to deposit $1,300 per month, starting one month from now, into a fixed rate account that pays 8% per year compounded semi-annually. How much will be in the account at the end of 23 years?

Answer 1

Answer

Annual Interest Rate = 8%
Semiannual Interest Rate = 4%

Effective Annual Rate = (1 + Semiannual Interest Rate)^2 - 1
= 1.04^2 - 1
= 1.0816 - 1
  = 0.0816 or 8.16%

Effective Monthly Rate = (1 + Effective Annual Rate)^(1/12) - 1
= 1.0816^(1/12) - 1
= 1.00656 - 1
= 0.00656 or 0.656%

Monthly Deposit = $1,300
Period = 23 years or 276 months

Accumulated Sum = $1,300 * FVIFA(0.656%, 276)
= $1,300 * (1.00656^276 - 1) / 0.00656
= $1,300 * 774.058972
= $1006276.66

At the end of 23 years, the account will be $1006276.66 or $1006277