
another annuity
 You wish to purchased a house for $120,000 in 12 years. You can invest your money at 4.5%/a compounded semiannually for the first 5 years and then you can get 6%/a compounded semiannually for the next 7 years. How much do you need to invest now? (Hint: start with the last 7 years)

another annuity
Quote:
Originally Posted by
euclid2  You wish to purchased a house for $120,000 in 12 years. You can invest your money at 4.5%/a compounded semiannually for the first 5 years and then you can get 6%/a compounded semiannually for the next 7 years. How much do you need to invest now? (Hint: start with the last 7 years)
For the last seven years,
interest, $\displaystyle i = \frac{6}{2}\%=3\%=0.03$
number of interest periods, $\displaystyle n = 7 \times 2 = 14$
The value of investment at the end of first five years
$\displaystyle = \frac {120 000}{(1.03)^{14}}$
$\displaystyle = \$79 334.14$
For the first five years,
interest, $\displaystyle i = \frac{4.5}{2}\%=2.25\%=0.0225$
number of interest periods, $\displaystyle n = 5 \times 2 = 10$
The present value of investment is
$\displaystyle = \frac {\$79 334.14}{(1.0225)^{10}}$
$\displaystyle = \$63 507.78$