ssignment Saved Problem 6-34 Calculating Annuity Payments [LO1] You want to be a

Question

ssignment Saved Problem 6-34 Calculating Annuity Payments [LO1] You want to be a millionaire when you retire in 35 years. a. How much do you have to save each month if you can earn an annual return of 10.7 b. How much do you have to save each month if you wait 15 years before you begin c. How much do you have to save each month if you wait 25 years before you begin percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) your deposits? (Do not round internediate calculations and round your answer to 2 decimal places, e.g., 32.16.) your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Savings per month starting today b. Savings per month starting in 15 years a. c Savings per month starting in 25 years

Explanation / Answer

Answer a We can use the future value of annuity due to calculate the savings per month required to become a millionaire in 35 years. Future value of annuity due = (1+r) x P{[(1+r)^n - 1]/r} P = Monthly savings = ? Future value of annuity due = 1 million i.e.10,00,000 r = monthly rate of return = 10.7%/12 = 0.008917 n = no.of months = 35 years x 12 = 420 1000000 = (1+0.008917) x P{[(1+0.008917)^420 - 1]/0.008917} 1000000 = 1.008917 x P[4554.68] 991162.14 = P[4554.68] P = 217.61 Savings per month starting today = $217.61 Answer b We can use the future value of annuity due to calculate the savings per month required to become a millionaire in 35 years. Future value of annuity due = (1+r) x P{[(1+r)^n - 1]/r} P = Monthly savings = ? Future value of annuity due = 1 million i.e.10,00,000 r = monthly rate of return = 10.7%/12 = 0.008917 n = no.of months = 20 years x 12 = 240 1000000 = (1+0.008917) x P{[(1+0.008917)^240 - 1]/0.008917} 1000000 = 1.008917 x P[832.06] 991162.14 = P[832.06] P = 1191.21 Savings per month starting in 15 years = $1191.21 Answer c We can use the future value of annuity due to calculate the savings per month required to become a millionaire in 35 years. Future value of annuity due = (1+r) x P{[(1+r)^n - 1]/r} P = Monthly savings = ? Future value of annuity due = 1 million i.e.10,00,000 r = monthly rate of return = 10.7%/12 = 0.008917 n = no.of months = 10 years x 12 = 120 1000000 = (1+0.008917) x P{[(1+0.008917)^120 - 1]/0.008917} 1000000 = 1.008917 x P[213.26] 991162.14 = P[213.26] P = 4647.63 Savings per month starting in 25 years = $4647.63

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