Question

An insurance settlement of $1 million must replace Trixie Eden's income for the next 35 years. What income will this settlement provide at the end of each month if it is invested in an antity that earns 8.3%, compounded monthly (a) Decide whether the problem relates to an ordinary annuity or an annuity due ordinary annuity annuity due (6) Solve the problem. (round your answer to the nearest cent) 5708336 X Need Help? TAT

Answer 1

1) Ordinary annuity:

income = monthly payment p

Formula:

$p=\frac{A_0q^n(q-1)}{q^n-1}$

where

$A_0$ = 1 million = $1,000,000

8.3% compounded monthly

$q=1+\frac{0.083}{12}=1.0069$

n=35*12=420

$p=\frac{(1000000)(1+\frac{0.083}{12})^{420}((1+\frac{0.083}{12})-1)}{(1+\frac{0.083}{12})^{420}-1}\\ =\frac{1000000\cdot \frac{0.083}{12}\left(\frac{0.083}{12}+1\right)^{420}}{\left(\frac{0.083}{12}+1\right)^{420}-1}\\ =\frac{125077.50510 }{1.00691 ^{420}-1} \\=7321.54$

Answer:

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