***Solve exercise using present value
principal -1500
term of invesment(%) -4.5
Interest compounded - monthly
present value ?
Compound interest ?
** the problem is asking for me to find the present value & compound value!!
Isn't 1500 already the present value?
Could you double check to see if there is a typo?
To solve for the present value and compound interest, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
- A is the future value (compound value)
- P is the principal (present value)
- r is the annual interest rate (converted to decimal)
- n is the number of times the interest is compounded per year
- t is the number of years
In this case, we have the following values:
Principal (P) = -1500 (negative because it represents an outgoing payment)
Annual interest rate (r) = -4.5% (negative because it is a decrease)
Interest compounded monthly, so n = 12
Term of investment = 1 year (t = 1)
Now let's plug in these values into the formula to find the present value (P) and compound value (A):
1. Compound Value (A):
A = P(1 + r/n)^(nt)
Convert the annual interest rate to a decimal: r = -4.5% = -4.5/100 = -0.045
A = -1500(1 + (-0.045)/12)^(12*1)
A = -1500(1 - 0.00375)^12
A = -1500(0.99625)^12
A ≈ -1500(0.95597)
A ≈ -1433.95
So, the compound value (A) is approximately -1433.95.
2. Present Value (P):
P = A / (1 + r/n)^(nt)
P = -1433.95 / (1 + (-0.045)/12)^(12*1)
P = -1433.95 / (1 - 0.00375)^12
P = -1433.95 / (0.99625)^12
P ≈ -1433.95 / (0.95597)
P ≈ -1500
The present value (P) is approximately -1500.
Therefore, the present value is -1500 and the compound value is -1433.95.