Business, 16.01.2021 16:10 atran4820

Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years, and the credit union pays an annual interest rate of 8%. A. Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn, if (1) $300 is deposited annually and the credit union pays interest annually. (2) $150 is deposited semiannually and the credit union pays interest semiannually. (3) $75 is deposited quarterly and the credit union pays interest quarterly. B. Use your finding in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.

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Answer from: bellagvjh1760

A(1) Future value of annual deposit = $4,345.97

A(2) Future value of semiannual deposit = $4,466.71

A(3) Future value of quarterly deposit = $4,530.15

B. The more frequent deposits and compounding of interest are, the higher the future value of an annuity of an annuity will be.

Explanation:

A(1). Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn if (1) $300 is deposited annually and the credit union pays interest annually.

These can be calculated using the Future Value (FV) of an Ordinary Annuity as follows:

FVA = P * (((1 + r)^n - 1) / r) (1)

Where,

FVA = Future value of the annual deposit = ?

P = Annual deposit = $300

r = Annual interest rate = 8%, or 0.08

n = number of years = 10

Substituting the values into equation (1), we have:

FVA = $300 * (((1 + 0.08)^10 - 1) / 0.08)

FVA = $4,345.97

A(2). Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn if (2) $150 is deposited semiannually and the credit union pays interest semiannually.

These can be calculated using the Future Value (FV) of an Ordinary Annuity as follows:

FVS = P * (((1 + r)^n - 1) / r) (2)

Where,

FVS = Future value of the semiannual deposit = ?

P = Semiannual deposit = $150

r = Semiannual interest rate = 8% / 2 = 0.08 / 2 = 0.04

n = number of semiannual = 10 * 2 = 20

Substituting the values into equation (2), we have:

FVS = $150 * (((1 + 0.04)^20 - 1) / 0.04)

FVS = $4,466.71

A(3). Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn if (3) $75 is deposited quarterly and the credit union pays interest quarterly.

These can be calculated using the Future Value (FV) of an Ordinary Annuity as follows:

FVQ = P * (((1 + r)^n - 1) / r) (3)

Where,

FVQ = Future value of the semiannual deposit = ?

P = Quarterly deposit = $75

r = Quarterly interest rate = 8% / 4 = 0.08 / 4 = 0.02

n = number of quarters = 10 * 4 = 40

Substituting the values into equation (3), we have:

FVQ = $75 * (((1 + 0.02)^40 - 1) / 0.02)

FVQ = $4,530.15

B. Use your finding in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.

Since the future value of quarterly deposit of $4,530.15 is greater than the future value of semiannual deposit of $4,466.71 which on its own is also greater than the future value of annual deposit of $4,345.97, this implies that the more frequent deposits and compounding of interest are, the higher the future value of an annuity will be.

Answer from: Quest

Pay attention in class and maybe you would know

Answer from: Quest

$527.7.if the following was the question $527.7 is the answer.students who are trying to raise funds have an agreement with a local pizza chain. the chain has agreed to sell them pizzas at a discount, which the students can then resell to families in the local community for a profit. it is expected that of the 500 families in the community, at most 70% will buy pizza. based on a survey of their personal preferences, the students believe that they should order no more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. they also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. they make a profit of $1.45, $1.75, and $1.98, respectively, for each cheese, pepperoni, and vegetarian pizza they resell. how many pizzas of each type should they buy?

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