Mr. Smith wants to save for his son’s college education.
If he deposits $300 each month at 12% compounded
monthly, how much (to the nearest penny) will he have in the
account after 8 years?
Answer = $
HOW DO I SOLVE THIS ??
You should know the "amount of an annuity" formula
amount = payment[ (1+i)^n - 1]/i
where i is the monthly rate, n is the number of payments
for your case
payment = 300
i = .12/12 = .01
n = 8(12) = 96
you do the button-pushing, let me know what you got.
To solve this problem, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount after 't' years
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, Mr. Smith deposits $300 each month (or $3,600 per year) at an annual interest rate of 12% compounded monthly. Therefore, we have:
P = $3,600
r = 12% = 0.12 (as a decimal)
n = 12 (monthly compounding)
t = 8 years
Substituting these values into the formula, we get:
A = $3,600(1 + 0.12/12)^(12 * 8)
Calculating within the parentheses:
A = $3,600(1 + 0.01)^(12 * 8)
Simplifying inside the parentheses:
A = $3,600(1.01)^(96)
Calculating 1.01 raised to the power of 96:
A ≈ $3,600 * 1.12682503013
Calculating the final amount:
A ≈ $4,056.57 (rounded to the nearest penny)
Therefore, Mr. Smith will have approximately $4,056.57 in the account after 8 years.
To solve this problem, we can use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (converted to decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, Mr. Smith is depositing $300 each month for 8 years at an annual interest rate of 12% compounded monthly. The monthly interest rate is found by dividing the annual interest rate by 12.
So, we have:
P = $300 (since that's the monthly deposit)
r = 12%/12 = 0.01 (monthly interest rate in decimal form)
n = 12 (compounded monthly)
t = 8 (number of years)
Plugging these values into the formula, we get:
A = $300(1 + 0.01/12)^(12*8)
Now, we can calculate the value of A using a calculator or computer program:
A = $300(1 + 0.01/12)^(12*8) ≈ $61466.95
Therefore, Mr. Smith will have approximately $61,466.95 in the account after 8 years.