Answer:
We should accept offer 2 because the amount today is higher than offer 1.
(offer 1 is $89,500, offer 2 is 91305)
Explanation:
To get the right answer we have to compare the 2 offers in the same moment of time. We use interest formula to bring the future amount to this moment.
First offer is for $89,500 today
Second offer is $35,000 today and $70,000 in two years discount rate is 11.5.
The formula of interest is A=P (1+r)ⁿ
A=Final amount
P= Principal ( deposit)
r= interest rate
n= time
We know A, r and n
Looking for P,
then P= A/(1+r)ⁿ
P= 70000/(1+0,115)² =56305
Offer 2 is =35000+56305=91305
The offer of $35,000 today and an additional guaranteed $70,000 two years from today will be accepted as the present value of the amount is higher than the first offer.
Present value refers to the current value of a sum of money that is discounted at a specified rate. The formula to calculate the present value of a future sum is:
[tex]\rm PV = FV\dfrac{1}{(1 + r)^n}[/tex] , where PV is the present value, FV is the future value, r is the discounting rate, and n refers to the number of years.
For the given question, the present value of the second offer can be calculated as:
The second offer consists of two sums, the present value should be calculated of the sum that will be received in the future:
[tex]\begin{aligned} \rm FV &= \$70,000\\\\r &= 11.5\%\\n &= 2\:years\\\end[/tex]
The present value will be:
[tex]\rm PV = FV\dfrac{1}{(1 + r)^n}\\\\\rm PV = 70,000\dfrac{1}{(1 + 0.115)^2}\\\\\\\rm PV = 70,000\dfrac{1}{1.2432245}\\\\\rm PV = 70,000\times 0.8044\\\\PV = \$56,305.197[/tex]
The total sum provides by offer second is:
[tex]\begin{aligned} \rm Total &= \$35,000 + \$56,305\\\\&= \$91,305\end[/tex]
Therefore the amount provided by the second offer is more than the first offer and hence the second offer should be accepted.
Learn more about present value here:
https://brainly.com/question/7331341
