Sarah wants to deposit $12,000 at the end of each year for 9 years into an annui

Question

Sarah wants to deposit $12,000 at the end of each year for 9 years into an annuity (a Sarah's local bank offers an account paying 9% interest compounded annually. Find he final amount she will have on deposit (b) Sarah's brother-in-law works in a bank that pays 6% compounded annually. If she deposits her money in this bank instead, how much money will she have in her account? (c) How much would Sarah lose over 9 years by using her brother-in-law's bank instead of her local bank? (a) Determine the correct annuity formula to use and substitute the values into the formula. Select the correct choice below and fill in the answers boxes to complete your choice (Type integers or decimals.)

Explanation / Answer

Answer a We can use the future value of annuity formula to calculate the amount of money in the account at the end of 9th year. FV of annuity = P * {[(1+r)^n - 1]/r} FV of annuity = future value of annuity = ? P = annual deposit = 12000 r = interest rate per annum = 9% n = no.of years = 9 FV of annuity = 12000 * {[(1+0.09)^9 - 1]/0.09} FV of annuity = 12000 * 13.02104 FV of annuity = 156252.44 Final amount Sarah will have in her bank account = $1,56,252.44 Answer b We can use the future value of annuity formula to calculate the amount of money in the account at the end of 9th year. FV of annuity = P * {[(1+r)^n - 1]/r} FV of annuity = future value of annuity = ? P = annual deposit = 12000 r = interest rate per annum = 6% n = no.of years = 9 FV of annuity = 12000 * {[(1+0.06)^9 - 1]/0.06} FV of annuity = 12000 * 11.49132 FV of annuity = 137895.79 Final amount Sarah will have in her bank account = $1,37,895.79 Answer c Sarah will loose $18,356.65 ($156252.44 - $137895.79) if she use her brother in law's bank instead of her local bank.

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