Answer:
$37685.56
Step-by-step explanation:
Given,
Total amount we want to accumulate,A = $500,000
Total time, we have,t = 30 years
Interest rate,r = 9%
We are asked to calculate how much money we should deposit to get the required amount after a certain time period.
So, according to compound interest formula,
[tex]A\ =\ P(1+r)^t[/tex]
Where, P = amount of money we need to deposit
[tex]=>\ 500,000\ =\ P(1+0.09)^{30}[/tex]
[tex]=>\ 500,000\ =\ P(1.09)^{30}[/tex]
[tex]=>\ 500,000\ =\ P\times 13.267[/tex]
[tex]=>\ \dfrac{500,000}{13.267}\ =\ P[/tex]
[tex]=>\ P\ =\ 37685.568[/tex]
So, we need to deposit total amount of $37,685.56.
