Respuesta :
Answer:
a.
Future Value in One Year = $1,070.00
Future Value in Two Years = $1,144.90
b.
Present Value of amount received in 1 year = $934.58
Present Value of amount received in 2 years = $873.44
The present value of the gift is less/lower if you get engaged in two years than it is if you get engaged in one year.
Explanation:
These can be done as follows:
Present Value Value in One Year Value in Two Years
Date Received (Dollars) (Dollars) (Dollars)
Today 1,000.00 1,070.00 1,144.90
In 1 year 934.58 1,000.00
In 2 years 873.44 1,000.00
a. Complete the first row of the table by determining the value of the gift in one and two years if you become engaged today.
To do this, we use future value (FV) formula as follows:
Future Value = A * (1 + r)^n ........................................ (1)
Where;
A = Amount received to day = $1,000.00
r = interest rate = 7%, or 0.07
n = number of years
Using equation (1), we therefore have:
Future Value in One Year = 1,000.00 * (1 + 0.07)^1 = $1,070.00
Future Value in Two Years = 1,000.00 * (1 + 0.07)^2 = $1,144.90
b. Complete the first column of the table by computing the present value of the gift if you get engaged in one year or two years.
To do this, we use present value (PV) formula as follows:
Present Value = A / (1 + r)^n ........................................ (2)
Where;
A = Amount received in specified year = $1,000.00
r = interest rate = 7%, or 0.07
n = number of years
Using equation (2), we therefore have:
Present Value of amount received in 1 year = 1,000.00 / (1 + 0.07)^1 = $934.58
Present Value of amount received in 2 years = 1,000.00 / (1 + 0.07)^2 = $873.44
Since $873.44 is less/lower than $934.58, we therefore have:
The present value of the gift is less/lower if you get engaged in two years than it is if you get engaged in one year.
The correct statement will be that the present value of the wedding gift is $873.43 if you get engaged in two years, then it is $934.57 if you get engaged in one year when the future value is $1000.
The future value of wedding gifts will be $1070.00 and $1144.9 at the end of first and second year respectively. The computation for the values can be done by applying values to the formula.
Calculation of future value and present value
- The present value of the gift can be calculated as using the formula below,
- [tex]\rm Present\ Value= \dfrac{Future\ Value}{1+ Fixed\ Interest\ Rate}\\\\\\\\\rm Present\ Value= \dfrac{\$1000}{1.07}\\\\\\\rm Present\ Value= \$ 934.57[/tex]
- The present value for one year is 934.57 USD.
- Now for two years,
- [tex]\rm Present\ Value= \dfrac{\$934.57}{1.07}\\\\\rm Present\ Value= \$873.43[/tex]
- Now to calculate the future value when the present value is considered to be as $1000. We will use the formula below,
- [tex]\rm Future\ Value\ for\ One\ Year=Present\ Value\ +\ \dfrac{Present\ Value\ x\ Time\ x\ Interest\ Rate}{100}\\\\\\\rm Future\ Value\ for\ One\ Year= 1000\ +\ \dfrac{1000\ \rm x\ 1\ \rm x\ 7}{100}\\\\\\\rm Future\ Value= \$1070[/tex]
- For the end of two years, the future value will be,
- [tex]\rm Future\ Value= Present\ Value\ (1+\dfrac{Interest}{no.\ of\ Compoundings})^n^t\\\\\\\rm Future\ Value= 1000\ (1+\dfrac{0.07}{1})^1^ x\ ^2\\\\\rm Future\ Value= \$1144.9[/tex]
Hence, the value of the gifts can be ascertained as per the calculations above.
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