What lump sum do 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? (Round your answer to the nearest cent.)

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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They need to deposit $31,172.49

Step-by-step explanation:

The compound interest formula is given by:

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 when

So

They need to deposit $31,172.49

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step-by-step explanation: