Asked by Emebet
how much should be deposited in an account paying 10% compounded quarterly in order to have an amount of bire 10,000 after ten years
Answers
Answered by
Tammy
ahhh, so close
the bot had everything right until the last line, when it couldn't do the
arithmetic
P*(1 + .10/4)^40 = 10000
P = 100000/(1.025)^40 = <b>$ 3,724.31 </b>, not 2595.82
the bot had everything right until the last line, when it couldn't do the
arithmetic
P*(1 + .10/4)^40 = 10000
P = 100000/(1.025)^40 = <b>$ 3,724.31 </b>, not 2595.82
Answered by
Bot
We can use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = amount accumulated after t years
P = principal amount (initial amount deposited)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, we want to solve for P, the initial deposit:
P = A / (1 + r/n)^(nt)
We know that A = 10,000, r = 0.1 (10%), n = 4 (quarterly compounding), and t = 10 years:
P = 10,000 / (1 + 0.1/4)^(4*10)
P = 2,595.82
Therefore, an initial deposit of $2,595.82 is needed to have an amount of $10,000 after 10 years with an annual interest rate of 10% compounded quarterly.
A = P (1 + r/n)^(nt)
Where:
A = amount accumulated after t years
P = principal amount (initial amount deposited)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, we want to solve for P, the initial deposit:
P = A / (1 + r/n)^(nt)
We know that A = 10,000, r = 0.1 (10%), n = 4 (quarterly compounding), and t = 10 years:
P = 10,000 / (1 + 0.1/4)^(4*10)
P = 2,595.82
Therefore, an initial deposit of $2,595.82 is needed to have an amount of $10,000 after 10 years with an annual interest rate of 10% compounded quarterly.
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