Questions: A father is trying to save for his daughter's wedding in two years. (Long engagement!). He thinks he can make the following contributions to an account: 12,610.00 today and 14,535.00 in one year. The father thinks he can earn 8.00% in the market each of the next two years. If the wedding is expected to cost 55,775.00 two years from today, how much will he need to contribute at the time of the wedding to cover its cost? A relative has promised to pay you 78.00 today, and he will pay you additional payments every year for the next five years. Each year he will add 68.00 to the previous payment. (So, the payment in year 1 will equal 146.00 ). You decide to save every dollar you are given and will invest the money in an account paying 4.00% annual interest. How much money will you have accumulated in five years? Keep in mind that you will have six total cash flows to invest.

A father is trying to save for his daughter's wedding in two years. (Long engagement!). He thinks he can make the following contributions to an account: 12,610.00 today and 14,535.00 in one year. The father thinks he can earn 8.00% in the market each of the next two years. If the wedding is expected to cost 55,775.00 two years from today, how much will he need to contribute at the time of the wedding to cover its cost? A relative has promised to pay you 78.00 today, and he will pay you additional payments every year for the next five years. Each year he will add 68.00 to the previous payment. (So, the payment in year 1 will equal 146.00 ). You decide to save every dollar you are given and will invest the money in an account paying 4.00% annual interest. How much money will you have accumulated in five years? Keep in mind that you will have six total cash flows to invest.
Transcript text: A father is trying to save for his daughter's wedding in two years. (Long engagement!). He thinks he can make the following contributions to an account: $\$ 12,610.00$ today and $\$ 14,535.00$ in one year. The father thinks he can earn $8.00 \%$ in the market each of the next two years. If the wedding is expected to cost $\$ 55,775.00$ two years from today, how much will he need to contribute at the time of the wedding to cover its cost? Submit Answer format: Currency: Round to: 2 decimal places. A relative has promised to pay you $\$ 78.00$ today, and he will pay you additional payments every year for the next five years. Each year he will add $\$ 68.00$ to the previous payment. (So, the payment in year 1 will equal $\$ 146.00$ ). You decide to save every dollar you are given and will invest the money in an account paying $4.00 \%$ annual interest. How much money will you have accumulated in five years? Keep in mind that you will have six total cash flows to invest. Submit Answer format: Currency: Round to: 2 decimal places.
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Solution

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Solution Steps

Question 1: Wedding Savings
  1. Calculate the future value of the initial contribution of $12,610.00$ after two years at an 8% annual interest rate.
  2. Calculate the future value of the second contribution of $14,535.00$ after one year at an 8% annual interest rate.
  3. Sum these future values to determine the total amount saved before the wedding.
  4. Subtract this total from the expected wedding cost to find the additional amount needed at the time of the wedding.
Step 1: Calculate the Future Value of the First Contribution

The father contributes \$12,610.00 today. We need to calculate its future value in two years with an 8% annual interest rate.

The formula for future value is: \[ FV = PV \times (1 + r)^n \]

Where:

  • \( PV = 12,610.00 \)
  • \( r = 0.08 \)
  • \( n = 2 \)

\[ FV_1 = 12,610.00 \times (1 + 0.08)^2 \] \[ FV_1 = 12,610.00 \times 1.1664 \] \[ FV_1 = 14,707.04 \]

Step 2: Calculate the Future Value of the Second Contribution

The father contributes \$14,535.00 in one year. We need to calculate its future value in one year with an 8% annual interest rate.

\[ FV_2 = 14,535.00 \times (1 + 0.08)^1 \] \[ FV_2 = 14,535.00 \times 1.08 \] \[ FV_2 = 15,697.80 \]

Step 3: Calculate the Total Future Value of Contributions

Add the future values of both contributions to get the total amount available for the wedding.

\[ FV_{\text{total}} = FV_1 + FV_2 \] \[ FV_{\text{total}} = 14,707.04 + 15,697.80 \] \[ FV_{\text{total}} = 30,404.84 \]

Step 4: Calculate the Additional Contribution Needed

The wedding is expected to cost \$55,775.00. Subtract the total future value of contributions from the wedding cost to find the additional amount needed.

\[ \text{Additional Contribution} = 55,775.00 - 30,404.84 \] \[ \text{Additional Contribution} = 25,370.16 \]

Final Answer for the First Question

\(\boxed{\text{Additional Contribution} = \$25,370.16}\)

Step 1: Calculate the Future Value of Each Payment

We need to calculate the future value of each payment made by the relative, considering the 4% annual interest rate.

Payment Today (\$78.00)

\[ FV_0 = 78.00 \times (1 + 0.04)^5 \] \[ FV_0 = 78.00 \times 1.2167 \] \[ FV_0 = 94.90 \]

Payment in Year 1 (\$146.00)

\[ FV_1 = 146.00 \times (1 + 0.04)^4 \] \[ FV_1 = 146.00 \times 1.1699 \] \[ FV_1 = 170.81 \]

Payment in Year 2 (\$214.00)

\[ FV_2 = 214.00 \times (1 + 0.04)^3 \] \[ FV_2 = 214.00 \times 1.1249 \] \[ FV_2 = 240.73 \]

Payment in Year 3 (\$282.00)

\[ FV_3 = 282.00 \times (1 + 0.04)^2 \] \[ FV_3 = 282.00 \times 1.0816 \] \[ FV_3 = 305.00 \]

Payment in Year 4 (\$350.00)

\[ FV_4 = 350.00 \times (1 + 0.04)^1 \] \[ FV_4 = 350.00 \times 1.04 \] \[ FV_4 = 364.00 \]

Payment in Year 5 (\$418.00)

\[ FV_5 = 418.00 \times (1 + 0.04)^0 \] \[ FV_5 = 418.00 \]

Step 2: Calculate the Total Future Value of All Payments

Add the future values of all payments to get the total amount accumulated in five years.

\[ FV_{\text{total}} = FV_0 + FV_1 + FV_2 + FV_3 + FV_4 + FV_5 \] \[ FV_{\text{total}} = 94.90 + 170.81 + 240.73 + 305.00 + 364.00 + 418.00 \] \[ FV_{\text{total}} = 1,593.44 \]

Final Answer for the Second Question

\(\boxed{\text{Total Accumulated Amount} = \$1,593.44}\)

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