Answer to Question #161163 in Financial Math for Mmm

Question

Carollynne has found her dream home in Pictou, Nova Scotia. It is selling for $500 000. When she retires 2 years from now, she plans to sell her present house for $450 000 and move. She decides to set aside $900 every two weeks until she retires in a fund earning 10.5%/a, compounded every second week. What is the difference between the future value of Carollynne’s investment and the extra $50 000 she needs for her dream home?

Answer 1

Solution:

We know, $A=\dfrac{R[(1+i)^n-1]}{i}$

Where, A is the amount, or future value, in dollars

R is the regular deposit, or payment, in dollars

i is the interest rate per compounding period, expressed as a decimal

n is the total number of deposits

Given, $R=\$ 900,\$

Rate is compounded every second week, means twice in a month.

There are 12 months in a year, and then n = 12 x 2 = 24 (as twice in a month)

So, $i=10.5\% \div 24=0.4375\%=0.004375$

Putting these values in formula of A, we get

$A=\dfrac{900[(1+0.004375)^{24}-1]}{0.004375}$

$A=\dfrac{900[(1.004375)^{24}-1]}{0.004375}=\dfrac{900[1.110456-1]}{0.004375}$

$A=\dfrac{900[0.110456]}{0.004375}=22722.38$

Now, required difference $=50000-22722.38=27277.62$

Hence, answer is $27,277.62