Answer:
a. $408,334.39
b. $3,457.40
Explanation:
r = rate per period = 8% = 0.08
P = Initial Value of Gift = $10,000
t = time = 30 - 5 = 25, As received after 5 years.
[tex]A = P (1 + r)^{t}[/tex]
[tex]A = $10,000 (1 + 0.08)^{25}[/tex]
[tex]A = $10,000 x 1.08^{25}[/tex]
A = $10,000 x 6.8485
A = $68,484.75
[tex]FV of annuity = P [\frac{(1 + r)^{n} - 1}{r} ][/tex]
P = Periodic Payment = $3,000
a.
n = number of periods = 30
[tex]FV of annuity = 3,000 [\frac{(1 + 0.08)^{30} - 1}{0.08} ][/tex]
[tex]FV of annuity = 3,000 [\frac{(1.08)^{30} - 1}{0.08} ][/tex]
[tex]FV of annuity = 3,000 [\frac{10.0627 - 1} {0.08} ][/tex]
[tex]FV of annuity = 3,000 [\frac{9.0627} {0.08} ][/tex]
FV of annuity = $3,000 x 113.2832
FV of annuity = $339,849.63
Accumulated value of money can be calculated as follows;
$68,484.75 + $339,849.63
$408,334.39
b.
If they wish to retire with $800,000 savings, they need to save additional amount of money every year to provide additional amount of money, as follows;
$800,000 - $68,484.75
$731,515.24
The extra annual savings can be calculated as follows;
[tex]731,515.24 = P [\frac{(1 + 0.08)^{30} - 1 }{0.08} ][/tex]
$731,515.24 = P x 113.28
Divide the above equation by 113.28 we get;
[tex]P = \frac{731,515.24}{113.28}[/tex]
P = $6,457.40
They are already paying $3,000, So the extra saving they need make every year is calculated as follows;
$6,457.40 - $3,000
$3,457.40
