Question

In: Finance

You want to save some money for graduate school. To do this you have decided that...

You want to save some money for graduate school. To do this you have decided that you will put $10,000 in the bank at the beginning of each of the next 7 years. The bank has agreed to pay you 8 percent nominal interest compounded annually. How much money will you have in the bank 7 years from today?

A. $17,138.24
B. $89,228.03
C. $96,366.28
D. $56,228.80
E. Something Else

You have just purchased a Scratch-and-Sniff lottery ticket. Scratching on the ticket, you discover that you have won a very large prize. The prize is paid in 20 equal annual installments of $5,000,000 each. You will receive the first payment one year from today. You are greedy though and decide that you would like to get your hands on as much money as you possibly can today. So you stop at the bank, before going to the lottery office, and tell them that you will give them all of the payments for a single lump sum today. The bank says they will buy the payments from you. The bank says they will use a 10 percent nominal annually compounded interest rate to calculate the present value of the payments, which is what you will receive. How much will the bank give you today?

A. $42,657,818.60
B. $46,824,600.46
C. $743,218.14
D. $100,000,000
E. Something Else

ou are planning a trip to Egypt at some point in the future. You will spend $50,000 on the trip. To achieve your goal of having enough money to take the trip, you have deposited $20,000 into the bank today. The account will earn 10 percent nominal interest compounded annually. You will take the trip immediately upon having $50,000 in the bank. How many years must you wait before you can take the trip?

A. 12.416
B. 25,000
C. 6.111
D. 9.614
E. It is not possible to solve the problem as the calculator gives an error.

Solutions

Expert Solution

To solve this problem, we can use the future value of annuity due formula:

Where,
FVA = Future Value of Annuity
A = Annuity / Payment
i = rate of interest
n = number of years

Substituting the values, we get:

So the answer is C.

We can use the formula of present value of annuity regular.

Where,
PVA = Present Value of Annuity
A = Annuity
i = rate of interest
n = number of years

Substituting the values, we get:

So he will get $42,567,818.60 today.

This amount looks similar to option A. If that is a typo then A is the answer otherwise E.

We can use the Future Value formula:

Where,
FV = Future Value
PV = Present Value
i = rate of return
n = number of periods

substituting the values, we get:

By using log on both sides we get:

...............................(you have to use financial calculator or excel here)

So the answer is D.

jeff jeffy answered 1 year ago

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