How much would you need to deposit in an account now in order to have $5000 in the account in 10 years? Assume the account earns 5% interest compounded weekly.
Question
How much would you need to deposit in an account now in order to have $5000 in the account in 10 years?
Assume the account earns 5% interest compounded weekly.
Solution
To solve this problem, we need to use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years
We know that A = $5000, r = 5% or 0.05 (in decimal), n = 52 (since interest is compounded weekly), and t = 10 years. We need to find P.
Rearranging the formula to solve for P gives us:
P = A / (1 + r/n)^(nt)
Substituting the known values gives us:
P = 5000 / (1 + 0.05/52)^(52*10)
Now, calculate the expression (1 + 0.05/52)^(52*10) first:
= (1 + 0.0009615384615384615)^520 = 1.647009500163776
Then, divide 5000 by this result:
P = 5000 / 1.647009500163776 P = $3035.05
So, you would need to deposit approximately 5000 in the account in 10 years, assuming the account earns 5% interest compounded weekly.
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