Your parents give you a gift of $14,000.00 on your 21st birthday.You invest this amount for 13 years at an interest rate of 9% pa, compounded quarterly.What is the final value of your investment?
Question
Your parents give you a gift of $14,000.00 on your 21st birthday.You invest this amount for 13 years at an interest rate of 9% pa, compounded quarterly.What is the final value of your investment?
Solution
To calculate the final value of the investment, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
where: A = the amount of money accumulated after n years, including interest. P = principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
Given: P = $14,000.00 r = 9% per annum = 0.09 (in decimal) n = compounded quarterly = 4 times per year t = 13 years
Substituting these values into the formula:
A = $14,000 (1 + 0.09/4)^(4*13)
Now, calculate the value inside the brackets:
= $14,000 (1 + 0.0225)^(52)
= $14,000 (1.0225)^(52)
Now, calculate the power:
= $14,000 * 1.905
Finally, multiply the principal amount by the calculated power:
= $26,670
So, the final value of your investment after 13 years would be approximately $26,670.
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