Computing loan repayment & Annuity,

David is a 40 year old South African . He obtains a loan from the local Bank on 1 January 2012. The terms and conditions of the loan are as follows:
Loan amount R 900 000
interest rates (p.a. effective):
7.97% for the first 7 years
12.38% for the next 8 years
11.49% for the last 5 years
The loan is repaid by level monthly payments in arrears for 20 years
David uses the loan to buy a house in Cape Town He leases the house to a tenant
starting from 1 February 2012. The lease agreement between David and the tenant
specified the following, among other things,
Lease period of 9 years from 1 February 2012
Initial monthly rent charge of R 6 120, rents are paid in advance
Rentals are to be reviewed annually. At each review date, the rentals increase at
a rate of the higher of 6% or inflation rate of the year prior to the rent review

The inflation rates are as follows:

1 5.70%
2 5.90%
3 6.00%
4 5.70%
5 6.40%
6 6.90%
7 6.00%
8 5.60%
9 7.00%
10 6.70%
11 6.40%
12 6.20%
13 6.00%
14 5.50%
15 6.90%
16 6.00%
17 7.00%
18 6.60%
19 5.70%
20 6.80%









David uses the rent to pay off the loan. If the rent is not enough to cover the loan
repayments, he pays off the balance out of his own pocket. Any excess funds are invested in Xiang Bank The funds invested earn 11.70% for the first 10 years and 12% % for the last 10 years. These rates are quoted per annum effective.
On 28 January 2017, the roof of the house is extensively damaged by strong winds.
Repairs cost R 8 950. David uses the funds from his investment in Xiang Bank to finance this. If the funds are not enough to pay for the repairs, David pays the balance using his personal funds. The repairs are completed and paid for on 1 February 2017.
After 8 years and 8 months, the tenant emigrates to Holland and the house stays
unoccupied for 3 months. David manages to do some renovations to the house during
this period. Renovations cost R 10 000 and are completed and paid for exactly one
month after the tenant had left. This is also taken from the investment in Xiang Bank.
Again, if the invested money is not enough to pay for the renovations, David pays the
balance using his personal funds. A new tenant comes exactly 3 months after the first one left. The duration of the lease is 10 years and 11 months and monthly rentals are paid in advance (starting at R10 250 per month). The rentals increase annually at a rate of the lower of 6.5% and the inflation rate of the year prior to the rent review.
After 20 years, David pays off the loan. The house is sold for R1 850 000. Selling
costs are 0.5% of the selling price. David needs some income for at least 25 years from
his age at that date(David will be aged 60 then). He will use the combined total of
the net sales proceeds and the accumulated value of the investments in Xiang Bank
to buy oating rate bonds and a guaranteed level annuity. The tax free level annuity,
payable monthly in arrears, is guaranteed for 25 years and is only found in the UK.
The spot rates for valuing the annuity are given in the `Assumptions' . The bonds are
also offered by the UK government. David wants to use 75% of his money to buy the
annuity and 25% to buy the bonds. The bonds are of a 25 year term and pay coupons of c% per annum, monthly in arrears. The coupons are subject to income tax (only) of t%. The yearly Rand-Pound exchange rates are given. Here Rand-Pound exchange rate shows the amount of South African Rands per British Pound. Assume here that the exchange rate re-
mains constant throughout each given year.The bonds are priced using b% p.a effective.

I have attached a workbook showing the various assumptions


Using the information provided,
1. Calculate the:
(i) monthly repayment
(ii) capital portion of the 188th payment
(iii) the total interest paid from the 5th year to the end of the 9th year.
2. Calculate the accumulated amount of the funds in Xiang Bank on 1 January
2032.
3. What is the price of a bond of R100 nominal (in pounds)?
4. How much does David receive (in Rands and net of tax) on his first monthly
coupon receipt from the UK government?
5. What is the amount of the level annuity David will receive each month (in
pounds)?
6. What is the total amount of money (in Rands and net of tax) that David will
receive from the bond investment over the 25 year period from the British
government bonds.

Your assistance regarding the above will be most appreciated

You were told that you must do the project yourself, I deem this to be against the rules, and upon finding out who you are with the help of the highly skilled IT department, you will be removed from the course, and will undergo a disciplinary hearing to establish whether you still have a place at UCT.
Regards,

Bosteer

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