calculate the present value (principal) and compound interest on $900 (term of investment 1.75 years ) rate of 18% compounded monthly
1.75 years = 21 months
monthly rate = .18/12 = .015
PV = 900(1.015)^-21 = $658.35
To calculate the present value and compound interest, we'll use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal (present value)
r = annual interest rate (as a decimal)
n = number of times compounded per year
t = number of years
Given:
Principal (P) = $900
Term (t) = 1.75 years
Interest rate (r) = 18% (or 0.18 as a decimal)
Compounded monthly (n = 12)
Step 1: Calculate the future value (A).
A = 900(1 + 0.18/12)^(12*1.75)
A ≈ 900(1 + 0.015)^21
A ≈ 900(1.015)^21
A ≈ 900(1.3616)
A ≈ $1,225.44
Step 2: Calculate the present value (Principal, P).
We'll rearrange the compound interest formula to solve for P.
P = A / (1 + r/n)^(nt)
P = 1225.44 / (1 + 0.18/12)^(12*1.75)
P ≈ 1225.44 / (1 + 0.015)^21
P ≈ 1225.44 / (1.015)^21
P ≈ 1225.44 / (1.3616)
P ≈ $900 (rounded)
The present value (principal) is approximately $900.
Step 3: Calculate the compound interest.
Compound Interest = A - P
Compound Interest ≈ $1,225.44 - $900
Compound Interest ≈ $325.44
The compound interest on the investment is approximately $325.44.
To calculate the present value and compound interest on an investment, we will need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (present value)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the money is invested for
Let's calculate the present value (principal) and compound interest step by step:
1. Convert the interest rate to decimal form:
The annual interest rate is given as 18%, so we divide it by 100 to convert it to a decimal:
r = 18/100 = 0.18
2. Calculate the number of times the interest is compounded per year:
The interest is compounded monthly, so n = 12 (compounded monthly means 12 times a year).
3. Calculate the future value of the investment:
We are given that the initial investment amount is $900 and the term of investment is 1.75 years.
Let's substitute the values into the formula:
A = $900(1 + 0.18/12)^(12 * 1.75)
A = $900(1 + 0.015)^(21)
A = $900(1.015)^(21)
A ≈ $1,114.21
4. Calculate the present value (principal):
Since we want to find the present value, we need to rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
P = $1,114.21 / (1 + 0.18/12)^(12 * 1.75)
P ≈ $762.47
5. Calculate the compound interest:
Compound Interest = A - P
Compound Interest = $1,114.21 - $762.47
Compound Interest ≈ $351.74
So, the present value (principal) of the investment is approximately $762.47, and the compound interest earned is approximately $351.74.