You deposit $10,000 in an account earning 4% interest compounded monthly.
a. How much will you have in the account in 25 years?
b. How much interest will you earn?
a. P = Po(1+r)^n.
Po = $10,000.
r = (4%/12) / 100% = 0.0033333 = Monthly
% rate expressed as a decimal.
n = 12Comp./yr * 25yrs = 300 Compounding
periods.
Plug the above values into the given
Eq.
Answer: P = $27,137.65.
b. I = P - Po
To calculate the future value of the account and the amount of interest earned, we can use the formula for compound interest:
Future Value = Principal × (1 + (Interest Rate / n))^(n × Time)
Interest Earned = Future Value - Principal
Where:
- Principal is the initial deposit ($10,000 in this case)
- Interest Rate is the annual interest rate (4% or 0.04 as a decimal)
- n is the number of compounding periods per year (in this case, monthly compounding, so n = 12)
- Time is the number of years (25 years in this case)
a. To calculate the future value of the account after 25 years:
Future Value = $10,000 × (1 + (0.04 / 12))^(12 × 25)
Future Value = $10,000 × (1.00333)^(300)
Future Value ≈ $18,331.21
b. To calculate the interest earned:
Interest Earned = $18,331.21 - $10,000
Interest Earned ≈ $8,331.21
Therefore, after 25 years, you would have approximately $18,331.21 in the account and earn approximately $8,331.21 in interest.