A savings account at Xyz bank offers 4% interest, compounded annually. How much money must I invest today in order for the account to grow to $5,000 in ten years? Answer to the nearest whole dollar.
P(1.04)^10 = 5000
solve for P
To calculate how much money you must invest today in order for the account to grow to $5,000 in ten years, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($5,000)
P = the principal amount (the amount you want to invest today)
r = the annual interest rate (4% as a decimal, so 0.04)
n = the number of times the interest is compounded per year (annually in this case)
t = the number of years (10 years)
We can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Now we can substitute the given values into the formula:
P = $5,000 / (1 + 0.04/1)^(1*10)
P = $5,000 / (1 + 0.04)^(10)
P = $5,000 / (1.04)^(10)
P ≈ $3,439.10
Therefore, you would need to invest approximately $3,439 today in order for the account to grow to $5,000 in ten years.