The Courters want to start saving for their son's college education. The estimated annual cost of attending UC Berkeley is $33,000 per year. Assuming it will take their son 5 years to graduate, and ignoring inflation, they will need at least $165,000.00. They have 16 years before their son will be ready for college. Their annuity pays
3% per year.
A) How much should be deposited monthly?
B) They decide to deposit $675.00 each month. How much is the future value of the account?
C) How much is from their deposits?
D) How much interest will be earned?
To find out how much should be deposited monthly, we can use the future value of an annuity formula:
FV = P * ((1+r)^n - 1) / r
Where:
FV = future value of the annuity
P = monthly deposit
r = annual interest rate
n = number of years
Given:
FV = $165,000.00
r = 3% = 0.03
n = 16 years
Substituting the values, we get:
$165,000.00 = P * ((1+0.03)^16 - 1) / 0.03
Solving for P, we find:
P = $165,000.00 * 0.03 / ((1+0.03)^16 - 1)
P ≈ $434.02
Therefore, the Courters should deposit approximately $434.02 monthly.
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To find out the future value of the account when they deposit $675.00 each month, we can use the same future value of an annuity formula.
Given:
P = $675.00
r = 3% = 0.03
n = 16 years
Substituting the values, we get:
FV = $675.00 * ((1+0.03)^16 - 1) / 0.03
Calculating the value, we find:
FV ≈ $205,010.62
Therefore, the future value of the account when they deposit $675.00 each month is approximately $205,010.62.
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To find out how much is from their deposits, we can multiply their monthly deposit by the number of months:
Deposits = $675.00 * 16 years * 12 months/year
Calculating the value, we get:
Deposits = $129,600.00
Therefore, approximately $129,600.00 is from their deposits.
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To find the total interest earned, we can subtract the total deposits from the future value of the account:
Interest = FV - Deposits
Interest = $205,010.62 - $129,600.00
Calculating the value, we find:
Interest ≈ $75,410.62
Therefore, approximately $75,410.62 will be earned in interest.