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.
a) How much would be in the account after six month if he took the $125,000.
b) Which option should he take?
c) How much more money does he gain in making this choice?
125,000 invested for 6 months
= 125000(1.025 = $128,125
So what do you think?
didn't see the "monthly" part
rate = .05/12 = .0041666...
amount = 125000(1.00416666...)^6 = $128,157.73
To answer these questions, we need to calculate the future value of $125,000 after six months of compounding interest at a 5% annual interest rate, compounded monthly. Let's break down the steps to find the answers:
a) How much would be in the account after six months if he took the $125,000?
To find the future value (FV) after six months, we can use the formula for compound interest:
FV = PV * (1 + (r/n))^(n*t)
Where:
FV = future value
PV = present value (initial amount)
r = annual interest rate (in decimal)
n = number of compounding periods per year
t = time in years
Given that Richard can invest the $125,000 at 5% interest compounded monthly (12 periods of compounding per year), we can calculate the future value:
PV = $125,000
r = 5% = 0.05
n = 12
t = 6 months = 0.5 years
FV = $125,000 * (1 + (0.05/12))^(12*0.5)
Calculating this expression will give us the answer.
b) Which option should he take?
To determine which option Richard should take, we need to compare the future value he would get by taking the $125,000 now and investing it at Valley Bank, and the $135,000 he would receive after six months.
By comparing the future value calculated in step a (from investing $125,000) with the future value of $135,000 (assuming no additional investment or interest), you can determine which option is more lucrative.
c) How much more money does he gain by making this choice?
To find out how much more money Richard gains by making a specific choice, you need to calculate the difference between the future value obtained by taking that choice and the other option.
Compare the future value obtained if Richard takes the $125,000 and invests it at Valley Bank to the $135,000 he would receive after six months to determine the monetary difference.
By following these steps, you can find the answers to the questions.