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