Question

1.Jack borrows $18,000 to be repaid in 3 equal year-end amounts over 3 years. If the interest rate is 11.9% per annum compounded quarterly, Jack’s annual repayment is (rounded to nearest dollar; don’t include the $ sign or commas):  

2.Jack needs $4900 in 6 years from today to buy a holiday. He invests $2700 today. Find the effective annual rate of interest that Jack needs to earn on this amount (as a %, 2 decimal places) in order to reach his goal.
(Solve using excel =RATE function; Answer in percentage to two decimals without the % sign e.g. 1.888 is 1.89)

3.Your uncle offers to sell you his vintage Rolls Royce. He suggests a payment plan where you pay just $18,000 today, $7100 in 8 months and $55,000 in exactly 21 months from today. If the interest rate is 14.9% per annum compounding monthly, what is the value of the offer (in present day dollars, rounded to the nearest dollar; don’t show $ sign or commas)?

4.You inherit $554,000. You can receive the $554,000 in one lump sum payment today or, alternatively, receive two amounts: $354,000 in 11 months and $220,000 in 21 months from today. If you can earn 5.7% per annum compounding monthly on your monies, what is the value of the option to receive two payments (in present day value)? (to nearest whole dollar,; don’t use $ sign or commas)

5.You join a gym for 2 years on a payment plan that requires you to pay $1,000 today, $170 in 8 months from today and $690 in 18 months from today. Alternatively you could pay $1800 today. If the interest rate is 6.2%p.a. compounding monthly, what is the advantage that the payment plan has over the upfront payment? (expressed in present day value rounded to the nearest cent; do not show $ sign or comma separators; if the payment plan is more costly than $1,800 today, your answer will show a negative eg. -300.35

6.Your business will pay you distributions of $18,000 in 9 months and another $11,000 in 19 months. If the discount rate is 6% per annum (compounding monthly) for the first 12 months, and 10% per annum (compounding monthly) for the next 7 months, what single amount received today would be equal to the two proposed payments? (answer to nearest whole dollar; do not use $ sign or commas)

Answer 1

1. Jack's equal annual repayment

is an annuity whose Present value, PV= $ 18000

at rate of interest, r= 11.9% p.a., ie. 11.9%/4=2.975% per quarter

for no.of payments, n=3*4=12 quarterly payments

we need to find the equal annual payment, Pmt.

so, using the PV of ordinary year-end annuity formula

PV=Pmt.*(1-(1+r)^-n)/r

& plugging-in all the known values,

18000=Pmt.*(1-(1+0.02975)^-12)/0.02975

Pmt.=18000/((1-(1+0.02975)^-12)/0.02975)=

1805.62

So, the equal annual payment

1805.62*4=

7222.48

(ANSWER)

2.Taking the geometric average return

(4900/2700)^(1/6)-1=

10.44%

(ANSWER)

NOTE: Excel =Rate function solves only annuities

3. interest rate /mth.=14.9%/12=1.2417% p.m.

Value of the offer (in present day dollars)=

18000+(7100/1.012417^8)+(55000/1.012417^21)=

66876.38738

66876

(ANSWER)

4..

Value of the option 1 in present day $

Lumpsum = 554000

Value of the option 2 in present day $

Monthly interest rate=5.7%/12=0.475% p.m.

PV of the option=(354000/1.00475^11)+(220000/1.00475^21)=

535181

Lumpsum receipt is greater in PV.

5. Interest rate per month=6.2%/12= 0.5167%

PV of payment plan 1=

1000+(170/1.005167^8)+(690/1.005167^18)=

1792.00

Alternate plan=

Lumpsum payment, 1800 today

Advantage that the 1st payment plan has over the upfront payment=

1800-1792= 8 (Answer)

6.. 6% p.a=6%/12=0.005 p.m. & 10% p.a.=10%/12=0.8333% p.m.

Single amount received today that would be equal to the two proposed payments=

(18000/1.005^9)+(11000/(1.005^12*1.00833^7))=

26986.33291

26986

(Answer)