if you invest $1 for 3 years in a term deposit with annual interest rate of 10% compounding every four months, the future value of the deposits at the end of the term will be _________________________.Round the result to 3 decimal place. Do not type the $ sign.
Solution
To calculate the future value of an investment with compounding interest, we use the formula:
FV = P * (1 + r/n)^(nt)
where:
- FV is the future value of the investment
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal form)
- n is the number of times that interest is compounded per year
- t is the time the money is invested for (in years)
In this case:
- P = $1
- r = 10% = 0.10
- n = 3 (since interest is compounded every four months, it means it is compounded three times a year)
- t = 3 years
Substituting these values into the formula, we get:
FV = 1 * (1 + 0.10/3)^(3*3)
Now, calculate the expression inside the parentheses:
1 + 0.10/3 = 1.03333
Then, raise this result to the power of 9 (3*3):
(1.03333)^9 = 1.34856
Finally, multiply this result by the principal amount (which is $1 in this case):
FV = 1 * 1.34856 = 1.34856
So, the future value of the deposit at the end of the term will be approximately $1.349 when rounded to three decimal places.
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