Final answer:
The future value of $20,000 after 12 years at a 1.6% annual interest rate compounded monthly is approximately $23,925.
Step-by-step explanation:
The student has asked about the future value of a sum of money when compounded monthly. To find out how much $20,000 will be worth after 12 years with an annual interest rate of 1.6% compounded monthly, we use the compound interest formula:
FV = P × (1 + r/n)nt
where:
- FV is the future value of the investment
- P is the principal amount ($20,000)
- r is the annual interest rate (1.6%, or 0.016)
- n is the number of times that interest is compounded per year (12, monthly)
- t is the number of years the money is invested (12)
Now we plug in the values:
FV = 20,000 × (1 + 0.016/12)12×12
Calculating this we get:
FV = 20,000 × (1 + 0.0013333)144
FV ≈ 20,000 × 1.196233
FV ≈ $23,925
Rounding to the nearest whole number, the future value would be approximately $23,925.