Question

Holly wants to have $200,000 to send a recently born child to college. She sets up a 529 plan and wants to know how much she must invest at the end of the year for the next 18 years if the funds can earn 5 percent. If she can earn 7 percent, how much less will she have to invest each year?

Answer 1

The amount Holly will have to invest less each year is $1,226.72.

Step-by-step explanation:

This can be calculated using the following 3 steps:

Step 1: Calculation of monthly payment at 5% interest rate

This can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:

FV = P_5% * (((1 + r)^n - 1) / r) ................................. (1)

Where,

FV = Future value or the amount Holly wants to have = $200,000

P_5% = Annual investment at 5% = ?

r = Annual interest rate = 5%, or 0.05

n = number of years = 18

Substituting the values into equation (1), we have:

$200,000 = P_5% * (((1 + 0.05)^18 - 1) / 0.05)

$200,000 = P_5% * 28.1323846738217

P_5% = $200,000 / 28.1323846738217

P_5% = $7,109.24

Step 2: Calculation of monthly payment at 7% interest rate

This can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:

FV = P_7% * (((1 + r)^n - 1) / r) ................................. (2)

Where,

FV = Future value or the amount Holly wants to have = $200,000

P_7% = Annual investment at 7% = ?

r = Annual interest rate = 7%, or 0.07

n = number of years = 18

Substituting the values into equation (2), we have:

$200,000 = P_7% * (((1 + 0.07)^18 - 1) / 0.07)

$200,000 = P_7% * 33.9990325104648

P_7% = $200,000 / 33.9990325104648

P_7% = $5,882.52

Step 3: Calculation of the amount Holly will have to invest less each year

Amount to invest less each year = P_5% - P_7%

Amount to invest less each year = $7,109.24 - $5,882.52

Amount to invest less each year = $1,226.72

Therefore, the amount Holly will have to invest less each year is $1,226.72.