# another annuity

• Sep 27th 2008, 05:25 PM
euclid2
another annuity
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) • Sep 27th 2008, 07:15 PM Shyam another annuity Quote: 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, $i = \frac{6}{2}\%=3\%=0.03$

number of interest periods, $n = 7 \times 2 = 14$

The value of investment at the end of first five years

$= \frac {120 000}{(1.03)^{14}}$

$= \79 334.14$

For the first five years,

interest, $i = \frac{4.5}{2}\%=2.25\%=0.0225$

number of interest periods, $n = 5 \times 2 = 10$

The present value of investment is

$= \frac {\79 334.14}{(1.0225)^{10}}$

$= \63 507.78$