On Joe Martin's graduation from college, Joe's uncle promised him a gift of $12000 in cash or $900 every quarter for the next 4 years after graduation. If money could be invested at 8% compounded quarterly, which offer is better for Joe?
I have done this problem but I keep getting to wrong answer for it and don't understand why?
Im getting the answer 339148.8 for the first part and 33914.88 for the second part but the book says the correct answers are 33914.88 and 33913.57. Help Please. ASAP I have a Math test tomorrow
I think Steve is missing part of the formula and/or using the wrong formula.
PV = paym(1 - (1+i)^-n)/i
so here
PV = 900(1 - 1.02^-16)/.02
= $12,219.94
So he should take the payment option.
12000(1+.08/4)^(4*4) = 16473.43
900*(1.02^16+1.02^15+...+1.02^1)
= 900(1.02^16 - 1)/(1.02-1)
= 16775.36
Have I missed something? My answers are about 1/2 the expected values.
I don't know it is really confusing. I am going to go talk to my teacher before class tomorrow.
ok that is right for the first part of the problem but apparently there are 2 parts
To determine which offer is better for Joe, we need to compare the present value of each offer. The present value is the current worth of a future sum of money, taking into account the time value of money and applicable interest rates.
First, let's calculate the present value of the $12,000 cash gift. We will use the formula for compound interest:
Present Value = Future Value / (1 + r/n)^(n*t)
Where:
Future Value = $12,000
r = 8% (converted to decimal form, so r = 0.08)
n = number of compounding periods per year = 4 (quarterly)
t = number of years after graduation = 0 (since the gift is immediately received)
Using these values, we can calculate the present value as follows:
Present Value = 12,000 / (1 + 0.08/4)^(4*0)
Present Value = 12,000 / (1 + 0.02)^0
Present Value = 12,000 / 1
Present Value = 12,000
So the present value of the $12,000 cash gift is simply $12,000.
Now, let's calculate the present value of receiving $900 every quarter for 4 years. We will use the same formula, but this time with different values:
Future Value = $900 (received every quarter for 4 years, so a total of 4 * 4 = 16 payments)
r = 8% (as before, r = 0.08)
n = 4 (quarterly)
t = 4 (4 years)
Present Value = 900 / (1 + 0.08/4)^(4*4)
Present Value = 900 / (1 + 0.02)^16
Present Value = 900 / (1.02)^16
Present Value = 900 / 1.3591386 (approximating to 8 decimal places)
Calculating this value, we get:
Present Value ≈ $662.0342451
Therefore, the present value of receiving $900 every quarter for 4 years is approximately $662.03.
Comparing the present values, we can see that the $12,000 cash gift has a higher present value than receiving $900 every quarter for 4 years. Hence, the better offer for Joe is the $12,000 cash gift.
I apologize for the confusion caused by the previous incorrect answers. The correct present value for receiving $900 every quarter for 4 years is approximately $662.03.