Question

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3. a) Consider an annuity of 6 cash flows of $5,000 payable annually. If the interest...

3. a) Consider an annuity of 6 cash flows of $5,000 payable annually. If the interest rate is 7 per cent per annum, what is the value of this annuity today if the first cash flow is to be paid immediately? [8 marks]

3. b) You are considering the purchase of a home for $700,000. You have available a deposit of $100,000. The bank will lend you money at 7 per cent per annum compounded monthly over a period up to 20 years. If you borrow the required funds over 20 years, what are the monthly repayments? After two years, how much do you still ow the bank? What is the interest component of the 25^th repayment? [7 marks]

Solutions

Expert Solution

Sol:

a) Present value of Annuity =

here,

C = cash flow per periods, = $5000

i = interest rate =7% or 0.07

n= number of payments =1 year

so, Present value of Annuity(after 1st year) = $5000 * [1-(1+0.07)^-1 ] / 0.07

= $5000 * [1-(1/1.07)] /0.07

= $5000 * [1- 0.9345] / 0.07

= $5000 * 0.0655/0.07

= $4678.57

b) Full amount required to purchase home = $700000

Amount available as deposit = $100000

Required fund from Bank as loan(P) =($700000 - $100000) = $600000

Interest rate(i) = 7% or 0.07

Period(n) = 20 years

Calculation of Monthly Payment:

Monthly payment formula

A = P * [ i (1+i)ⁿ/ (1+i)ⁿ- 1]

Monthly Payments(A)= $600000 * [0.07 (1+0.07)²⁰ / (1+0.07)²⁰ -1]

A = $4651.79

Calculation of interest component of the 25^th repayment:

the interest component of the 25^th repayment = $3,327.45

Periods	Beginning Balance	Interest	Principal	Ending Balance
1	$600,000.00	$3,500.00	$1,151.79	$598,848.21
2	$598,848.21	$3,493.28	$1,158.51	$597,689.69
3	$597,689.69	$3,486.52	$1,165.27	$596,524.42
4	$596,524.42	$3,479.73	$1,172.07	$595,352.36
5	$595,352.36	$3,472.89	$1,178.90	$594,173.45
6	$594,173.45	$3,466.01	$1,185.78	$592,987.67
7	$592,987.67	$3,459.09	$1,192.70	$591,794.97
8	$591,794.97	$3,452.14	$1,199.66	$590,595.31
9	$590,595.31	$3,445.14	$1,206.65	$589,388.66
10	$589,388.66	$3,438.10	$1,213.69	$588,174.97
11	$588,174.97	$3,431.02	$1,220.77	$586,954.19
12	$586,954.19	$3,423.90	$1,227.89	$585,726.30
Year #1 End
13	$585,726.30	$3,416.74	$1,235.06	$584,491.24
14	$584,491.24	$3,409.53	$1,242.26	$583,248.98
15	$583,248.98	$3,402.29	$1,249.51	$581,999.47
16	$581,999.47	$3,395.00	$1,256.80	$580,742.68
17	$580,742.68	$3,387.67	$1,264.13	$579,478.55
18	$579,478.55	$3,380.29	$1,271.50	$578,207.05
19	$578,207.05	$3,372.87	$1,278.92	$576,928.13
20	$576,928.13	$3,365.41	$1,286.38	$575,641.75
21	$575,641.75	$3,357.91	$1,293.88	$574,347.86
22	$574,347.86	$3,350.36	$1,301.43	$573,046.43
23	$573,046.43	$3,342.77	$1,309.02	$571,737.41
24	$571,737.41	$3,335.13	$1,316.66	$570,420.75
Year #2 End
25	$570,420.75	$3,327.45	$1,324.34	$569,096.41

Calculation of Balance Owe to the bank after 2nd year:

Periods	Beginning Balance	Interest	Principal	Ending Balance
1	$600000	$41547.82	$14273.66	$585726.30
2	$585726.30	$40515.97	$15305.51	$570420.75

jeff jeffy answered 1 year ago

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