Help...Please...
You buy a commemorative coin for $25. The value of the coin increases 3.25% per year. How much will the coin be worth in 15 years? Round to the nearest cent.
To calculate the value of the coin in 15 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = The final amount
P = The starting amount (principal)
r = The annual interest rate (as a decimal)
n = The number of times interest is compounded per year
t = The number of years
In this case:
P = $25 (starting value)
r = 3.25% per year, which is 0.0325 as a decimal
n = 1 (interest is compounded annually)
t = 15 years
Let's calculate the final amount:
A = $25(1 + 0.0325/1)^(1*15)
A = $25(1 + 0.0325)^(15)
A = $25(1.0325)^(15)
A ≈ $25(1.588643911)
A ≈ $39.716097775
Rounding to the nearest cent, the coin will be worth approximately $39.72 in 15 years.
To find out how much the coin will be worth in 15 years, we need to calculate the value after each year and keep compounding the growth.
The value of the coin increases by 3.25% per year, which means it grows at a rate of 0.0325. To calculate the future value of the coin, we use the formula for compound interest:
Future Value = Present Value * (1 + Interest Rate)^Number of Years
In this case:
- Present Value (PV) is $25, the initial purchase price.
- Interest Rate (r) is 0.0325, the annual growth rate.
- Number of Years (n) is 15, the number of years in which the coin's value will increase.
Now that we have the values, let's plug them into the formula:
Future Value = $25 * (1 + 0.0325)^15
Calculating the expression inside the parenthesis:
(1 + 0.0325) = 1.0325
Now, let's raise that to the power of 15 (since the coin's value increases for 15 years):
Future Value = $25 * 1.0325^15
Evaluating 1.0325 raised to the power of 15 (using a calculator):
Future Value ≈ $25 * 1.609810474 ≈ $40.24526285
Rounding this value to the nearest cent, the coin will be worth approximately $40.25 in 15 years.