Gerald has taken out a loan of $100,000 today to start a
business. He has agreed to repay the loan on the following
terms:
• Repayments will be made on a monthly basis. The first
repayment will be made exactly one month from today.
• The repayments for the first 5 years will cover interest
only to help reduce the financial burden for Gerald’s business at
the start.
• After the 5-year interest-only period, Gerald will make
level monthly payments that will fully repay the loan after an
additional 15 years (i.e. 20 years from today, the loan will be
fully repaid).
• The interest charged is 5% p.a. effective.
Using this information, answer the following questions.
The equivalent effective monthly rate on the loan =
0.4176%
The size of the first repayment due exactly one month from
now = $416.7
The size of the level repayments that occur after the
initial 5-year
interest-only period = 790.81 per month
10 years have passed, and Gerald’s business is doing well.
Further, he has made all the repayments on his loan so far as
described above, and has just made the repayment due today.
However, it has just been announced that the interest rate on
Gerald’s loan will go up to 5.5% p.a. compounding
semi-annually.
d)
Calculate the new equivalent effective monthly rate on the
loan
e)
Calculate the current loan outstanding (again, it is 10 years after
the loan was initially taken out). Note that the new interest rate
only applies from today onwards.
f)
Because Gerald’s business is doing well, he decides to repay a lump
sum of $10,000 immediately. To further reduce the amount of
interest he is paying to the bank, he will increase his monthly
repayments to $1,000 per month.
How many full
repayments of $1,000 does Gerald have to make in order to fully
repay this loan? (Note: Gerald may need to make a further, smaller
payment in the subsequent month)
g)
Calculate the size of the smaller payment.
PLEASE SHOW WORKING (NOT EXCEL FORMULAE) – thank
you