Your friend turned out to be dishonest and was looking to con you out of $4,902,714. After clearing your mind and refocusing, you decide to calculate how much money you would need to put aside at the beginning of each month for the next 30 years in order to have $4,902,714. You estimate conservatively that your money will earn 2% a year, compounded monthly. What will your monthly contribution to the account need to be?
Question 6. Your friend turned out to be dishonest and was looking to con you out of $4,902,714. After clearing your mind and refocusing, you decide to calculate how much money you would need to put aside at the beginning of each month for the next 30 years in order to have $4,902,714. You estimate conservatively that your money will earn 2% a year, compounded monthly. What will your monthly contribution to the account need to be?
Future Value of Annuity Due = P * [ (1+r)^n - 1 ] /r * (1+r)
Where,
P = Monthly Deposit
r =rate of interest per period i.e. 2%/12 = 0.1666% or 0.001666
n = no. of compounding period i.e. 30 years * 12 =360
Future Value of Annuity Due = P * [ (1+r)^n - 1 ] /r * (1+r)
4,902,714 = P * [ (1+0.001666)^360 - 1 ] /0.001666 * (1+0.001666)
4,902,714 = P * [ (1.001666)^360 - 1 ] /0.001666 * (1.001666)
4,902,714 = P * [1.821209 - 1 ] /0.001666 * (1.001666)
4,902,714 = P * (0.821209/0.001666) *(1.001666)
4,902,714 = P * 492.7254 * (1.001666)
4,902,714 = P * 493.5466
P = 4,902,714/493.5466
P = 9,933.64
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