Question

Multiple compounding periods: Samantha is looking to invest some money, so that she has $5,500 at the end of three years. Which investment should she make given the following choices: a. 4.2% compounded daily b. 4.9% compounded monthly c. 5.2% compounded quarterly d. 5.4% compounded annually

Answer 1

Samantha should choose that investment option which lets her invest the lowest initial amount and yet have her targeted investment value of $ 5500 at the end of 3 years.

(a) 4.2 % compounded daily. Daily compounding rate = 4.2 / 365 = 0.01151 %

Number of Days in three years = 3 x 365 = 1095 days

Let the initial investment be M

Therefore, M = 5500 / (1.0001151)^(1095) = $ 4848.75

(b) 4.9 % compounded monthly.

Monthly Compounding Rate = (4.9 / 12) = 0.4083 %

Number of months in three years = 12 x 3 = 36 months

Let the intial investment be $ M

Therefore, M = 5500 / (1.004083)^(36) = $ 4749.59

(c) 5.2 % compounded quarterly

Quarterly Compounding Rate = (5.2/4) = 1.3 %

Number of Quarters in three years = 4 x 3 = 12 years

Let the initial investment be $ M

Therefore, M = 5500 / (1.013)^(12) = $ 4710.31

(d) 5.4 % compounded annually

Let the initial investment be $ M

Therefore, M = 5500 / (1.054)^(3) = $ 4697.22

As the initial investment for the fourth option is the lowest, Samantha will go with the fourth option.