If a nurse deposits $2,000 today in a bank account and the interest is compounded annually at 10 percent, what will be the value of this investment:
a. five years from now?
B. ten years from now?
C. fifteen years from now?
D. twenty years from now?
I will do the first, you do the rest the same way
a) amount = 2000(1.10)^5 = 3221.02
b) ...
To calculate the value of the investment over different time periods, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial investment or principal amount ($2,000 in this case)
r = the annual interest rate (10% or 0.10)
n = the number of times the interest is compounded per year (since it is compounded annually, n = 1)
t = the number of years
Let's calculate the value of the investment for different time periods:
a. Five years from now:
t = 5
A = 2000(1 + 0.10/1)^(1*5)
A = 2000(1.10)^5
A ≈ $3,105.85
b. Ten years from now:
t = 10
A = 2000(1 + 0.10/1)^(1*10)
A = 2000(1.10)^10
A ≈ $6,727.50
c. Fifteen years from now:
t = 15
A = 2000(1 + 0.10/1)^(1*15)
A = 2000(1.10)^15
A ≈ $13,443.25
d. Twenty years from now:
t = 20
A = 2000(1 + 0.10/1)^(1*20)
A = 2000(1.10)^20
A ≈ $26,432.05
Therefore, the value of the investment will be approximately:
a. Five years from now: $3,105.85
b. Ten years from now: $6,727.50
c. Fifteen years from now: $13,443.25
d. Twenty years from now: $26,432.05
To find the value of an investment with compounded interest, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the nurse deposits $2,000, the interest is compounded annually at 10% (0.10 as a decimal), and we need to calculate the future value for various time periods.
a. Five years from now:
Substituting the values into the formula:
A = 2000(1 + 0.10/1)^(1*5)
A = 2000(1.10)^5
A ≈ $3,105.85
b. Ten years from now:
A = 2000(1 + 0.10/1)^(1*10)
A = 2000(1.10)^10
A ≈ $6,727.50
c. Fifteen years from now:
A = 2000(1 + 0.10/1)^(1*15)
A = 2000(1.10)^15
A ≈ $13,439.20
d. Twenty years from now:
A = 2000(1 + 0.10/1)^(1*20)
A = 2000(1.10)^20
A ≈ $26,374.03
Therefore:
a. Five years from now, the value of the investment will be approximately $3,105.85.
b. Ten years from now, the value of the investment will be approximately $6,727.50.
c. Fifteen years from now, the value of the investment will be approximately $13,439.20.
d. Twenty years from now, the value of the investment will be approximately $26,374.03.