1. 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) 2. another annuity Originally Posted by euclid2 1. 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\$