(Future Value) Suppose you invest $8000 into an account that pays an annual interest rate of 6.2%. How much is in the account after 30 years if
a. simple interest is compound monthly?
b. interest is compounded monthly?
c. interest is compounded daily?
P*(1+i)* Exponent which is time invested
$8000x(1+.o62)30
$8000 x ((1 + .062)^30) = $48,621.1794 U.S. dollars
To calculate the future value of an investment using different compounding periods, we will use the formula:
Future Value = Principal * (1 + (Interest Rate / n)) ^ (n * t)
Where:
- Principal is the initial amount invested
- Interest Rate is the annual interest rate
- n is the number of compounding periods per year
- t is the number of years
Let's calculate the future value for each case:
a. Simple Interest is Compound Monthly:
In this case, since simple interest is being compounded monthly, the interest rate remains unchanged throughout the year.
Principal: $8000
Interest Rate: 6.2% (or 0.062 as a decimal)
Compounding Period: Monthly (n = 12)
Number of Years: 30 (t = 30)
Future Value = $8000 * (1 + (0.062 / 12)) ^ (12 * 30)
b. Interest is Compounded Monthly:
When the interest is compounded monthly, the interest is added to the account balance every month.
Principal: $8000
Interest Rate: 6.2% (or 0.062 as a decimal)
Compounding Period: Monthly (n = 12)
Number of Years: 30 (t = 30)
Future Value = $8000 * (1 + (0.062 / 12)) ^ (12 * 30)
c. Interest is Compounded Daily:
If interest is compounded daily, the compounding period is even smaller, and interest is added to the account balance daily.
Principal: $8000
Interest Rate: 6.2% (or 0.062 as a decimal)
Compounding Period: Daily (n = 365)
Number of Years: 30 (t = 30)
Future Value = $8000 * (1 + (0.062 / 365)) ^ (365 * 30)
Simply perform the calculations using the given formula, and you will find the future value for each case.