Don has just received a cash gift of $70,000 from his rich eccentric uncle. He wants to set it aside to pay for his daughter Cynthia's college education. Cynthia will begin college in 13 years and Don's financial advisor says that she can earn 8% interest on an investment in a special college fund. How much will Don have in the fund when Cynthia begins college?
70000*1.08^13 = ____
190373.7
Well, with 70,000 dollars, Don could buy a lot of textbooks with funny-looking math symbols on the cover. But if he decides to invest it for his daughter's college education, let’s calculate how much he'll have in the fund in 13 years!
Using the power of humor and math, we can determine the future value of the investment. Given the interest rate of 8%, we'll need to use the wonderful concept of compound interest. Don't worry, we'll do the math for you!
Assuming the interest is compounded annually, the future value can be calculated using the formula:
FV = P(1 + r/n)^(n*t)
Where:
FV = future value
P = initial principal (amount invested)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $70,000
r = 0.08 (8% as a decimal)
n = 1 (compounded annually)
t = 13 years
Now, let's apply some clown math!
FV = $70,000 * (1 + 0.08/1)^(1*13)
After crunching the numbers and making funny faces, we find that Don will have approximately $193,246.05 in the college fund when Cynthia begins her higher education adventure.
So, with a bit of compound interest magic, Don can smile knowing that he'll have a decent chunk of change to help Cynthia face the hilarious world of college expenses!
To calculate the future value of Don's investment after 13 years with an interest rate of 8%, we can use the compound interest formula:
Future Value = Present Value * (1 + Interest Rate)^Number of Periods
In this case, the present value is $70,000, the interest rate is 8%, and the number of periods is 13 years. Plugging these values into the formula, we have:
Future Value = $70,000 * (1 + 0.08)^13
Now let's calculate this step by step:
Step 1: Add 1 to the interest rate.
1 + 0.08 = 1.08
Step 2: Raise this sum to the power of the number of periods.
1.08^13 = 2.65096413
Step 3: Multiply the present value by the result from step 2.
$70,000 * 2.65096413 = $185,067.49
Therefore, when Cynthia begins college, Don will have approximately $185,067.49 in the college fund.
To calculate the amount Don will have in the college fund when Cynthia begins college, we can use the concept of compound interest. Compound interest is the interest earned on the initial investment (principal) as well as the accumulated interest from previous periods.
To calculate the future value of an investment with compound interest, we can use the formula:
FV = PV * (1 + r/n)^(nt)
where:
FV = future value
PV = present value (initial investment)
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Let's apply this formula to Don's situation.
PV (present value) = $70,000
r (interest rate) = 8% = 0.08 (as a decimal)
n (compounding frequency) = 1 (assuming it's compounded once a year)
t (number of years) = 13
Now, plug in the values in the formula:
FV = 70,000 * (1 + 0.08/1)^(1*13)
Simplifying the calculation:
FV = 70,000 * (1.08)^13
Using a calculator or a spreadsheet, calculate:
FV ≈ $201,324.36
Therefore, Don will have approximately $201,324.36 in the college fund when Cynthia begins college.