**Question No 1**

**a) If your aunt accepted your proposal, how much would she be willing to lend you today**

Aunt Amy has two options either accept the proposal or deposited the amount into bank

There are two assumptions

- Rate of interest on deposited amount is 2 %
- Rate of interest on loan is 6 %

The following payment will be made to Aunt Amy which also includes the rate of interest at 6

In the above table a four-year cash payment schedule is given. The cash paid to Aunt Amy also included the rate of interest or interest as well. All the cash payments are also discounted at 6 % interest rates. The difference between the cash payments and discounted amount is the actual interest paid to aunt Amy. The total cash payment made to Aunt Amy is $165,000 and the total present value of these payments is $ 141,289.295. So keeping the above assumptions the total amount she will give as loan would be $ 141,289.295, and if cash payment is not discounted than the total amount she would lend is $165,0000.

**b) How much would your aunt have in four (4) years if she chooses not to lend you the money**

If aunt Amy refused to lend money than on the basis of the following assumptions at 2% interest rate should would have the following balance at the end of the four years. There are two assumptions

- Rate of interest on deposited amount is 2 %
- Rate of interest on loan is 6 %

So on the above assumptions if she has total $165,000 balance at the moment and wants to deposit it into bank account then she will get 2% interest on its balance. In this case the future value of the after four years is followed.

**Case No 1**

Future Value = Present Value x (1+Rate of interest) ^n

Present Value = 165,000

Rate of interest = 2%

Number of Period = 4 Years

Future Value = 165,000 x (1+.02) ^4

= 165,000 x 1.08243216

= $178,601.3064

**Case No 2 **

Future Value = Present Value x (1+Rate of interest) ^n

Present Value = 141289.2953

Rate of interest = 2%

Number of Period = 4 Years

Future Value = 141289.2953 x (1+.02) ^4

= 141289.2953 x 1.08243216

= $152,936.0770

**c) How much would your aunt have in four (4) years if she chooses to lend you the money?**

**Case No 1**

Again there would be assumption in this case as well. If aunt Amy will lend $165,000 that at the end of four years she will have the following balance.

Future Value = Present Value x (1+Rate of interest) ^n

Present Value = 165,000

Rate of interest = 6%

Number of Period = 4 Years

Future Value = 165,000 x (1+.06) ^4

= 165,000 x 1.26247696

= $208,308.6984

The amount she will have at the end of four years = $208,308.6984

**Case No 2**

Future Value = Present Value x (1+Rate of interest) ^n

Present Value = 141289.2953

Rate of interest = 6%

Number of Period = 4 Years

Future Value = 141289.2953 x (1+.06) ^4

= 141289.2953 x 1.26247696

= $178,374.4800

The amount she will have at the end of four years = $178,374.4800

**d) Based on your calculations in parts (b) and (c), you believe your aunt should be indifferent between lending you the money or putting the money in the bank. Discuss whether she would agree with your assessment. **

Based on the above calculations there is huge difference between lending and depositing the money into the bank account. If aunty Amy deposit the money into bank account, then she will get $178,601 on 165,000 and in case if she lends the money than she will get $208,308.6984 on 165,000.

The following table and graph shows the difference between depositing into bank account and lending the money.

The above chart shows the interest earned on both options lending and depositing the money. The aunt Amy will earn more if she lends the money at 6 % interest rate rather depositing into bank account.

**e)**

She is willing to lend money on 6 % interest rate. The principal amount would be either 165,000 or 141289.2953 based on the cash payments.

**f) You and your aunt eventually agree to an interest rate of 4%. Explain whether you win, whether your aunt wins, and how such an outcome can be possible.**

In this particular case both the parties won. If aunty Amy deposit money into the bank account, then she would have get only 2 % interest on the balance. On the other side getting loan on 4% rather 6 % is also remarkably good.

a) Monthly Gross Income = $ 3853 / .60 = 6421.827

b)

c) The calculations done in part b is absolutely correct. The amount paid by the borrower can be calculated through multiplied the number of period with monthly payments. The grand total after multiplication will be the total amount paid by the borrower. The difference between principal amount and the grand total is the interest paid by the borrower on the loan.

d) There is a different interest charge on both car loan for Mercedes A-Class Saloon and private condominium. The interest rate for car loan is 1.6 % and for private condominium is 1.8 %. So in this regards car loan is cheaper than private condominium. The car financing loan is .20% cheaper than the housing loan.

Interest rate = House loan – car financing loan

= 1.8 % -1.6 % = .20 %

e) The interest loan charged by the banks are different due its market value and demand. In order to attract the banks customers, bank offer different products and services on different interest rates. If the demand of the product or services is higher in the market than the interest rate will also be higher otherwise lower. If loan is taken for the longer period than banks has to face the risk for the long period of time. So in this particular case bank will charge higher interest rate.

In this particular case, the house loan is taken for the longer period of time which means that bank has to face the risk for longer period along with amount is higher than car financing. Though both these house and car are assets in nature but the total value and time period is different. That is why in house loan rate of interest is higher comparatively to car financing.

**Question No 3**

a) What is the breakeven age for the BRS plan?

The breakeven age for the BRS is followed.

Initial investment = $ 90,500

Monthly Payment = $780

Interest rate = 4 %

Age at the initial investment = 55

Present Value at the age of 55 = 780PVAF (4/12, 12n) PVF (4/12, 120)

= 780 PVAF (4/12, 12n) 0.6708

For Breakeven Age Initial Investment = PV of payouts

90,500 = 780 PVAF (4/12, 12n) 0.6708

90,500 / (0.6708 * 780) = PVAF (4/12, 12n)

PVAF (4/12, 12n) = 77.83 = 172.9660

PVAF (4/12. 258) = 172.86 Therefore we can take n = 258 months = 258 / 12 = 21.5 years

Hence breakeven age = 55 + 21.5 = 76.5 years

b)

Now we have I = 181,000

Monthly payout = 1,440 other things remain same.

Therefore, for breakeven age

181,000 = 1,440 PVAF(4/12%,12n) 0.6708

PVAF (4/12%, 12n) = 181,000 / (1,440 *0.6708)

PVAF (4/12%, 12n) = 187.38 By using Financial Calculator

PVAF (4/12%, 12n) = 187.23

Therefore, n = 293 /12 = 24.4

Hence breakeven age = 55 + 24.4 = 79.4 year

c)

Initial investment – PV of payouts is equal under both the options

90,500 – 780* PVAF (4/12%, 12n) *0.6708 = 181,000 – 1,440 PVAF (4/12% 12n) *0.6708

{1440 PVAF (4/12% 12n) – 780 PVAF (4/12% 12n)} 0.6708 = 181,000 – 90,500

660 PVAF (4/12% 12n) 0.6708 = 90,500

PVAF (4/12%, 12n) = 90,500 / (660 * 0.6708) PVAF (4/12% 12n) = 204.41

By using financial calculator, we find that when 12n = 341

PVAF (4/12%, 12n) = 204.34

Therefore, n = 341 /12 = 28.42

Hence the life expectancy for indiﬀerence between these two plans is 55 + 28.42

= 83.42 years

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