Question

The Government of Ghana is raising funds for a road construction project. The Minister of Finance is considering the flexibility that 91-day financing affords, even though this means they will have to roll-over funds borrowed at possibly higher interest rate. The flexibility that short-term financing affords is that Government can pay-off the loan whenever it comes into money, something that would be expensive if it borrowed long-term.

1. If GHS 71 million is needed today for the 3-year project and the most recent treasury bill report published in the dailies reports the 91-day ‘interest rate’ as 24.09% p.a., what is the compound annual rate?
2. How much must government payback to investors in 91 days if it borrows?
3. How much in interest will government pay upfront?
4. If rates remain the same for three years and investors roll-over principal and interest, how much will government have to pay at the end?
5. What if investors rollover principal only?

Answer 1

i)Compounded annual Rate:

91day interest rate =(24.09*(91/365))=6.006%

There are four 91 days period in a year

Compounded Annual Rate =((1+0.06006)^4)-1=0.262763=26.28%(Rounded to two decimals)

ii)Amount to be paid back to the investors=71million*(1+0.06006)=75.26426 million GHS

iii) Amount of Interest to be paid =75.26426-71=4.26426 million GHS

iv) Amount to be paid at the end of 3 years if payments rolled over=71*((1+0.262763)^3)=142.963079 million GHS

v)If only principal is rolled over, amount of interest of 4.26426 millions to be paid every 91 days and 71 million to be paid at the end of three years