b) An investment grows according to the formula A=P(1+r)nt, where A is the final amount, P is theprincipal, r is the interest rate, n is the number of times compounded per year, and t is the time inyears. If P=5000, r=0.03, n=4, and t=10, find the final amount after 10 years.
Question
b) An investment grows according to the formula A=P(1+r)nt, where A is the final amount, P is theprincipal, r is the interest rate, n is the number of times compounded per year, and t is the time inyears. If P=5000, r=0.03, n=4, and t=10, find the final amount after 10 years.
Solution
To find the final amount after 10 years, we can substitute the given values into the formula A=P(1+r/n)^(nt).
Here, P = 5000 (the principal amount), r = 0.03 (the interest rate), n = 4 (the number of times compounded per year), t = 10 (the time in years).
So, the formula becomes:
A = 5000(1+0.03/4)^(4*10)
First, calculate the value inside the bracket:
1 + 0.03/4 = 1.0075
Then, raise this value to the power of 40 (4 times 10):
(1.0075)^40 ≈ 1.3161
Finally, multiply this result by the principal amount:
A = 5000 * 1.3161 ≈ 6580.5
So, the final amount after 10 years would be approximately $6580.5.
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