. Richard Simons is selling his house. He has a choice of taking $125,000 today or $135,000 in 6 months. If he takes the money today, he can invest it at Valley Bank at 5% interest compounded monthly.How much would the 125,000 be worth in six months if invested?Which offer should he take? Why? How much more money does he gain in
making this choice?
value of 125000 6 months from now
= 125000(1.00416666...)^6
= 128157.73
Pr value of 135000
x(1.00416666..)^6 = 135000
x = 131673.68
So both solutions show that he should take the 135000 six months from now.
At he present time, the difference is worth
= 131673.68 - 125000
$ 6673.68
Six months from now the difference is worth
135000 - 128157.73 =6842.27
notice that
6673.68(1.00416666..)^6 = 6842.27
To determine how much the $125,000 would be worth in six months if invested at 5% interest compounded monthly, we need to use the compound interest formula. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (5% in this case)
n = the number of times that interest is compounded per year (12 times for monthly compounding)
t = the number of years the money is invested for (0.5 years in this case)
Substituting the values into the formula, we get:
A = 125,000 * (1 + (0.05/12))^(12 * 0.5)
A = 125,000 * (1.0041667)^(6)
Calculating this, we find that the future value of the $125,000 investment after six months would be approximately $125,522.08.
Now let's compare this with the alternative offer of $135,000 in six months. Since the future value of the investment is less than $135,000, Richard should choose to take the $135,000 offer in six months. This is because the $135,000 is greater than the amount he would have by investing the $125,000.
Therefore, by choosing the $135,000 offer, Richard gains an additional amount of $135,000 - $125,522.08, which is approximately $9,477.92.