Question

4. New parents wish to save for their newborn's education and wish to have $36,000 at the end of 19 years. How much should the parents place at the end of each year into a savings account that earns an annual rate of 7.1% compounded annually? (Round your answers to two decimal places.)
$   953.27
How much interest would they earn over the life of the account?
$   17887.87
Determine the value of the fund after 11 years.
$   15126.05
How much interest was earned during the 11th year?
$ I can't get this part

5. A corporation creates a sinking fund in order to have $620,000 to replace some machinery in 11 years. How much should be placed in this account at the end of each month if the annual interest rate is 4.7% compounded monthly? (Round your answers to the nearest cent.)
$   3595.95
How much interest would they earn over the life of the account?
$   145334.44
Determine the value of the fund after 2, 4, and 6 years.

2 years	90304.00	$
4 years	189490.13	$
6 years	298432.02	$

How much interest was earned during the second month of the 4th year?
$ I don't understand this part

Answer 1

First question is being answered here:

1. (a) Here, the deposits will be same every year, so it is an annuity. The future value of annuity is $36000. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)n  - 1 / r)

where, FVA is future value of annuity = $36000, P is the periodical amount, r is the rate of interest = 7.1% and n is the time period = 19

Now, putting these values in the above formula, we get,

$36000 = P * ((1 + 7.1%)19 - 1 / 7.1%)

$36000 = P * ((1 + 0.071)19 - 1 / 0.071)

$36000 = P * ((1.071)19 - 1 / 0.071)

$36000 = P * ((3.68128927704 - 1 / 0.071)

$36000 = P * (2.68128927704 / 0.071)

$36000 = P * 37.7646377049

P = $36000 / 37.7646377049

P = $953.27

So, the amount of money that we need to deposit each year is $953.27

(b) Interest earned = Future value - Total deposits

Total deposits = $953.27 * 19 = $18112.13

Future or accumulated value = $36000

Putting these values in the above equation, we get,

Interest earned = $36000 - $18112.13 = $17887.87

(c) Here, the deposits will be same every year, so it is an annuity. We need to calculate the future value of annuity . We will use the future value of annuity formula as per below:

FVA = P * ((1 + r)n  - 1 / r)

where, FVA is future value of annuity, P is the periodical amount = $953.27, r is the rate of interest = 7.1% and n is the time period = 11

Now, putting these values in the above formula, we get,

FVA = $953.27 * ((1 + 7.1%)11 - 1 / 7.1%)

FVA = $953.27 * ((1 + 0.071)11 - 1 / 0.071)

FVA = $953.27 * ((1.071)11 - 1 / 0.071)

FVA = $953.27 * ((2.12659201652 - 1 / 0.071)

FVA = $953.27 * (1.12659201652 / 0.071)

FVA = $953.27 * 15.8674931904

FVA = $15126.05

So, value of the fund after 11 years will be $15126.05.

(d) Interest earned = Future value - Total deposits

Total deposits = $953.27 * 11 = $10485.97

Future or accumulated value = $15126.05

Putting these values in the above equation, we get,

Interest earned = $15126.05 - $10485.97 = $4640.08