can someone help with these compound interest problems? bonus if you can show ho
ID: 2527337 • Letter: C
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can someone help with these compound interest problems? bonus if you can show how you got your answer.
Problem 5 Time Value of Money Applications 8 points Part A Smith Trucking won a settlement in a lawsuit and was offered $100,000 today by the defendant's insurance company. The insurance company also offered two other alternatives. Determine the amount from each of the following alternatives that Smith should use to compare to the $100,000. Assume an interest rate of 7% with interest ns compounded annually, Support your answer s with the approprtate calculations ment made at the end of the year) Il) A lump sum payment of $200,000 at the end of the eleventh year Part B Sally's grandmother is going to give her a gift when she graduates from college in four years. The grandmother told Sally she can have $25,000 at the end of the fourth year or she can choose from either of the two following alternatives. Determine the amount from each of the alternatives that Sally should use to compare to the $25,000. Assume an interest rate of 7% with interest compounded annually. Support each answers with appropriate computations. A payment of $18,000 today. $6,000 at the end of each year for the next four years.Explanation / Answer
Part A
Value offered today by defendant’s insurance company = $100,000
Alternative 1 (value today): -
$25000 per year for the next 5 years (payment at the end of the year)
$25000 are future inflows.
Hence, we will apply present value of annuity today formulae i.e.
P = A[(1/i) – 1/{i(1+i)^n}]
Where, P = present value = ?
A = future inflows = $25000
i = interest rate = 0.07
n = number of years. = 5
P = $25000[(1/0.07)-1/{0.07(1+0.07)^5}]
= $102,500
Alternative 2 (value today): -
Lump sum payment of $200,000 at the end of eleventh year
Hence, we will apply present value formulae i.e.
P = A/(1+r)^n
Where, P = present value = ?
A = future inflow = $200,000
i = interest rate = 0.07
n =at number of years. = 11
P = $200,000/(1+0.07)^11
= $95018.56
Ans: - Comparing $100,000 with alternative 1 and 2, Highest value is offered in alternative 1 of $102500. Hence, Smith trucking should go with alternative 1.
Part B
Value offered by grandmother to sally at the end of forth year = $25,000
Alternative 1 (value at the end of fourth year): -
Payment of $18,000 today
Hence, we will apply future value formulae i.e.
A = P x (1+r)^n
Where, A = future value = ?
P = present value = $18,000
i = interest rate = 0.07
n =at number of years. = 4
A = $18000 x (1+ 0.07)^4
= $23594.32
Alternative 2 (value at the end of fourth year): -
Hence, we will apply future value of annuity formulae i.e.
FV = A[{(1+r)^n-1}/r]
Where, FV = future value = ?
A = present inflows = $6,000
r = interest rate = 0.07
n = number of years = 4
FV = $6,000[{(1+0.07)^4-1}/0.07]
= $26639.65
Ans: - Comparing $25,000 with alternative 1 and 2, Highest value is offered in alternative 2 of $26639.65. Hence, Sally should go with alternative 2.
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