all has always dreamed of opening a café by the seaside. he decides he will save to help open the café by…

all has always dreamed of opening a café by the seaside. he decides he will save to help open the café by depositing money in an ordinary annuity that earns 7.2% interest, compounded annually. deposits will be made at the end of each year. how much money will he need to deposit into the annuity each year for the annuity to have a total value of $26,000 after 9 years? do not round intermediate computations, and round your final answer to the nearest cent. if necessary, refer to the list of financial formulas.

all has always dreamed of opening a café by the seaside. he decides he will save to help open the café by depositing money in an ordinary annuity that earns 7.2% interest, compounded annually. deposits will be made at the end of each year. how much money will he need to deposit into the annuity each year for the annuity to have a total value of $26,000 after 9 years? do not round intermediate computations, and round your final answer to the nearest cent. if necessary, refer to the list of financial formulas.

Answer

Explanation:

Step1: Recall the future - value of an ordinary annuity formula

The formula for the future value of an ordinary annuity is ( FV = A\times\frac{(1 + r)^{n}-1}{r}), where (FV) is the future value of the annuity, (A) is the annual payment (deposit), (r) is the interest rate per period, and (n) is the number of periods.

We are given that (FV=$26000), (r = 0.072) (since (7.2%=0.072)), and (n = 9). We need to solve for (A).

First, rewrite the formula for (A): (A=\frac{FV\times r}{(1 + r)^{n}-1})

Step2: Substitute the given values into the formula

Substitute (FV = 26000), (r=0.072), and (n = 9) into the formula:

((1 + r)^{n}=(1 + 0.072)^{9})

Using the formula (a^{b}=e^{b\ln(a)}), (\ln(1.072)\approx0.0696), (b\ln(a)=9\times0.0696 = 0.6264), (e^{0.6264}\approx1.871)

((1 + 0.072)^{9}-1\approx1.871-1 = 0.871)

(A=\frac{26000\times0.072}{0.871})

(26000\times0.072 = 1872)

(A=\frac{1872}{0.871}\approx2149.25)

Answer:

($2149.25)