Answer:
Future value will be larger with smaller compounding period; $373.4 more would be earned with shorter compounding period.
Explanation:
Given:
Amount to be invested = 29,000÷2 = $14,500
Duration if amount invested = 25 years
Rate = 4% or 0.04 compounded annually
Value of investment at the end of 25 years = [tex]14,500\times(1+0.04)^{25}[/tex]
= $38,654.63
Future value if compounded annually is $38,654.63
Future value if semi-compounded annually:
Duration = 25×2 = 50 periods
Rate = 0.04÷2 = 0.02
Value of investment at the end of = [tex]14,500\times(1+0.02)^{50}[/tex]
= $39,028.03
Future value if semi-compounded annually is $39,028.03
As such, future value is larger if compounding period was 6 months.
They would have earned $373.40 more that is (39,028.03 - 38,654.63), with shorter period.
