Respuesta :
Answer:
They need to deposit $31,172.49
Step-by-step explanation:
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time the money is invested or borrowed for, in years.
In this problem
We want to find P for which [tex]A = 100000[/tex] when [tex]r = 0.09, n = 12, t = 13[/tex]
So
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]100000 = P(1 + \frac{0.09}{12})^{12*13}[/tex]
[tex]3.208P = 100000[/tex]
[tex]P = \frac{100000}{3.208}[/tex]
[tex]P = 31172.49[/tex]
They need to deposit $31,172.49
The lump sum the parents need to deposit in an account earning 9%, compounded monthly, so that it will grow to $100,000 for their son's college fund in 13 years is approximately $31, 172. 49 to the nearest cent.
using compound interest formula:
p = A/ (1 + r /n)ⁿˣ
where
p = principal
Amount = A = 100,000
x = time = 13 years
n = 12
Rate = r = 9% = 0.09
Therefore,
p = 100,000 / (1 + 0.09/12)¹²ˣ¹³
p = 100, 000 / (1.0075 )¹⁵⁶
p = 100,000 / 3.20795709275
P = 31172.4876612
p ≈ 31, 172. 49
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