1. You\'re trying to save to buy a new $207,000 Ferrari. You have $57,000 today

Question

1. You're trying to save to buy a new $207,000 Ferrari. You have $57,000 today that can be invested at your bank. The bank pays 6.5 percent annual interest on its accounts.

How long will it be before you have enough to buy the car? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

2. Imprudential, Inc. has an unfunded pension liability of $584 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present.

If the relevant discount rate is 7.7 percent, what is the present value of this liability? (Enter your answer in dollars not in millions. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

3. Rust Bucket Motor Credit Corporation (RBMCC), a subsidiary of Rust Bucket Motor, offered some securities for sale to the public on March 28, 2008. Under the terms of the deal, RBMCC promised to repay the owner of one of these securities $100,000 on March 28, 2037, but investors would receive nothing until then. Investors paid RBMCC $23,799 for each of these securities; so they gave up $23,799 on March 28, 2008, for the promise of a $100,000 payment 29 years later.

Based on the $23,799 price, what rate was RBMCC paying to borrow money? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)

Suppose that, on March 28, 2020, this security’s price is $42,080. If an investor had purchased it for $23,799 at the offering and sold it on this day, what annual rate of return would she have earned? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

If an investor had purchased the security at market on March 28, 2020, and held it until it matured, what annual rate of return would she have earned? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)

%

4.You have just made your first $4,700 contribution to your retirement account. Assume you earn an 13 percent rate of return and make no additional contributions.

What will your account be worth when you retire in 32 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What if you wait 10 years before contributing? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Based on the $23,799 price, what rate was RBMCC paying to borrow money? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)

Explanation / Answer

(‘1)

We know that

FV= PV x (1+r)n

FV/PV= (1+r)n

In (FV/PV)= n x In (1+r)

Here FV= $207000, PV= $57000, r= 6.5 % , n= number of periods ( required data)

In the absence of specific information it is assumed that compounding of interest is annual.

In (207000/57000) = n x In (1.065)

In ( 3.6316)= n x In (1.065)

1.29= n x 0.0630

‘n= 20.48 Years

(‘2)

We know that

PV= FV x 1/ (1+r)n

PV= 584 x (1.077) -20

PV= 584 x 0.2268

PV= $ 132.46

(Assumed that compounding of interest is annual)

                (‘3) (a)

We know that

FV= PV x ( 1+r )n

‘r= ( FV/PV)1/n -1

‘r= ( 100000/23799) 1/29 -1

‘r=( 4.2019 )0.03448-1

‘r= 1.05-1

‘r= 0.05 ( i.e. 5 % per annuam)

‘(3) (b)

PV= 23799, FV= 42080 n= 12 years

‘r= ( FV/PV)1/n -1

“r= ( 42080/23799)1/12 -1

‘r= 5 %,

‘(3 )(c )

PV= 42080, FV= 100000, n= 17 Years

‘r= ( FV/PV)1/n -1

“r= ( 100000/42080)1/17 -1

‘r= 0.05 ( i.e 5 %)

‘(4)(a)

FV= PV x (1+r)n

FV= 4700 x ( 1.13)32

FV= 4700 x 49.9471

FV= $ 234751.32

‘(4) (b)

When 10 years is waited then revised period will be 22 years

FV= 4700 x (1.13)22

FV= 4700 x 14.7138

FV= $ 69155

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