Tanisha wants to have $1000 in her bank account in 5 years. How much money should she deposit if her account earns 6% interest which is compounded 2 times per year?
Sum = P(1+i)^n
where Sum = the accumulated sum
P = the amount deposited
i = the periodic decimal interest rate
n = the number of compounding periods
Therefore, Sum = 5000(1+.06/2)^(5x2)
To determine how much money Tanisha should deposit, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, which is $1000 in this case
P = the principal amount (the initial deposit)
r = the annual interest rate (as a decimal), which is 6% or 0.06 in this case
n = the number of times that interest is compounded per year, which is 2 times in this case
t = the number of years
We need to rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Substituting the known values into the formula:
P = 1000 / (1 + 0.06/2)^(2*5)
Now we can calculate the value:
P = 1000 / (1 + 0.03)^(10)
P = 1000 / (1.03)^10
P = 1000 / 1.344074
P ≈ $744.10
Therefore, Tanisha should deposit approximately $744.10 in her bank account to reach her goal of $1000 in 5 years, considering the given interest rate and compounding period.