# Thread: ammount of an annuity2

1. ## ammount of an annuity2

You wish to purchased a house for $200,000 in 12 years. You can invest your money at 5%/a compounded semiannually. How much do you need to invest every 6 months, starting in 6 months, so that you will have$200,000 at the time of your last deposit? (Hint: You need to find the value for "a". )

2. Originally Posted by euclid2
You wish to purchased a house for $200,000 in 12 years. You can invest your money at 5%/a compounded semiannually. How much do you need to invest every 6 months, starting in 6 months, so that you will have$200,000 at the time of your last deposit? (Hint: You need to find the value for "a". )
It is an increasing annuity with

Rent, R = ?

Future value, F = $200 000 interest, $i = \frac{5}{2}\% = 0.025$ number of pay periods, $n = 12 \times 2 = 24$ Future value, $F = \frac {(1+i)^n - 1}{i} \times R$ $200 000 = \frac {(1.025)^{24} - 1}{0.025} \times R$ $R = \frac{200 000 \times 0.025}{(1.025)^{24} - 1}$ R =$6182.56