A woman wishes to invest $5,800.She can buy saving bonds
at a bank with an annual interest rate of 2% compounded monthly for a period of 5 years. This means that her investment will grow with compound interest over the 5-year period.
To calculate the future value of her investment, we can use the formula for compound interest:
Future Value = Principal x (1 + (Rate / n))^(n x Time)
Where:
- Principal = $5,800
- Rate = 2% or 0.02
- n = number of times interest is compounded per year, which is 12 for monthly compounding
- Time = 5 years
Plugging in the values:
Future Value = $5,800 x (1 + (0.02 / 12))^(12 x 5)
Future Value = $5,800 x (1 + 0.00166667)^60
Future Value = $5,800 x (1.00166667)^60
Future Value = $5,800 x 1.10980
Future Value = $6,443.24
Therefore, after 5 years of investing $5,800 in saving bonds with a 2% annual interest rate compounded monthly, the woman's investment will grow to approximately $6,443.24.