
present value
 Calculate the present value for each section using compound interest. A) You need $1,000 in 8 years. You can invest your money at 3%/a compounded semiannually.
B) You need $200 in 30 months. You can invest your money at 6%/a compounded monthly.
C) You need $15,000 in 12.5 years. You can invest your money at 4%/a compounded quarterly.

Quote:
Originally Posted by
euclid2  Calculate the present value for each section using compound interest. A) You need $1,000 in 8 years. You can invest your money at 3%/a compounded semiannually.
A) Future value, F = $1000
interest, $\displaystyle i = \frac{3}{2} \% = 0.015$
number of interest periods, $\displaystyle n = 8 \times 2 = 16$
Present value, P = ?
Future value, $\displaystyle F = (1+i)^n.P$
Present value, $\displaystyle P = \frac {F}{(1+i)^n}$
$\displaystyle P = \frac {1000}{(1.015)^{16}}$
Now, finish up.

Quote:
Originally Posted by
euclid2  Calculate the present value for each section using compound interest.
B) You need $200 in 30 months. You can invest your money at 6%/a compounded monthly.
B) Future value, F = $200
interest, $\displaystyle i = \frac{6}{12} \% = 0.005$
number of interest periods, $\displaystyle n = 30$
Present value, P = ?
Future value, $\displaystyle F = (1+i)^n.P$
Present value, $\displaystyle P = \frac {F}{(1+i)^n}$
$\displaystyle P = \frac {200}{(1.005)^{30}}$
Now, finish up.

Quote:
Originally Posted by
euclid2  Calculate the present value for each section using compound interest.
C) You need $15,000 in 12.5 years. You can invest your money at 4%/a compounded quarterly.
C) Future value, F = $15,000
interest, $\displaystyle i = \frac{4}{4} \% = 1\% = 0.01$
number of interest periods, $\displaystyle n = 12.5 \times 4 = 50$
Present value, P = ?
Future value, $\displaystyle F = (1+i)^n.P$
Present value, $\displaystyle P = \frac {F}{(1+i)^n}$
$\displaystyle P = \frac {15000}{(1.01)^{50}}$
Now, finish up.