Question

Anthony and Michelle Constantino just got married and received ​$29,000 in cash gifts for their wedding. How much will they have on their​ twenty-fifth anniversary if they place half of this money in a​ fixed-rate investment earning 4 percent compounded annually. Would the future value be larger or smaller if the compounding period was 6​ months? How much more or less would they have earned with this shorter compounding​ period?

Answer 1

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 = $14,500\times(1+0.04)^{25}$

                                                                         = $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 = $14,500\times(1+0.02)^{50}$

                                                                         = $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.