Business, 18.03.2021 02:30 nayelieangueira

You want to have Br. 10,000,000 when you retire in 40 years. You expect to earn 12% compounded semiannually over the entire 40-year period. How much extra money per month must you deposit if you choose to fund using an ordinary annuity technique rather than an annuity due technique?

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You must deposit Br. 54.01 extra per month if you choose to fund using an ordinary annuity technique rather than an annuity due technique.

Explanation:

This can be determined using the following 3 steps:

Step 1: Calculation of monthly deposit under ordinary annuity

Theis can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity given as follows:

FV = Do * (((1 + r)^n - 1) / r) (1)

Where,

FV = Future value of the amount = Br. 10,000,000

Do = Semiannual deposit under ordinary annuity = ?

r = Semiannual interest rate = Annual interest rate / Number of semiannuals in a year = 12% / 2 = 6%, or 0.06

n = number of semiannuals = Number of years * Number of semiannuals in a year = 40 * 2 = 80

Substituting the values into equation (1) and solve for Do, wee have:

10,000,000 = Do * (((1 + 0.06)^80 - 1) / 0.06)

10,000,000 = Do * 1746.59989136857

Do = 10,000,000 / 1746.59989136857

Do = Br. 5,725.40972286698

Mo = Monthly deposit under ordinary annuity = Do / Number of months in a semiannual = Br. 5,725.40972286698 / 6 = Br. 954.23

Step 2: Calculation of monthly deposit under annuity due

Theis can be calculated using the formula for calculating the Future Value (FV) of an Annuity Due given as follows:

FV = Dd * (((1 + r)^n - 1) / r) * (1 + r) (2)

Where

Dd = Semiannual deposit under annuity due = ?

Other values are as already defined in Step 1 above.

Substituting the values into equation (2) and solve for Dd, wee have:

10,000,000 = Dd * (((1 + 0.06)^80 - 1) / 0.06) * (1 + 0.06)

10,000,000 = Dd * 1,851.39588485068

Dd = 10,000,000 / 1,851.39588485068

Dd = Br. 5,401.329927233

Md = Monthly deposit under annuity due = Dd / Number of months in a semiannual = Br. 5,401.329927233 / 6 = Br. 900.22

Step 3: Calculation of difference between monthly deposit under ordinary annuity and monthly deposit under annuity due

Difference = Mo - Md = Br. 954.23 - Br. 900.22 = Br. 54.01

Therefore, you must deposit Br. 54.01 extra per month if you choose to fund using an ordinary annuity technique rather than an annuity due technique.

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