Respuesta :
Answer:
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.
