Final answer:
To calculate the accumulated debt of Tanzania after 10 years, the constant annual gap of 2 million shillings and the compounding annual interest of 12% on the growing debt must be considered. The yearly debt increases by the new shortfall and the interest accrued from the previous year's debt. A financial calculator or spreadsheet is typically used for this compound interest calculation.
Step-by-step explanation:
The government of Tanzania plans to spend 10 million shillings while anticipating net taxes of 8 million shillings, leaving a shortfall of 2 million shillings yearly. Financing this gap requires issuing 10-year government bonds at a 12% interest rate. Each subsequent year, the government must not only cover the gap between spending and taxes but also the interest on the accumulated debt.
To calculate the accumulated debt after 10 years, we need to consider both the constant annual shortfall and the compounding interest on the debt. Here's the calculation:
- Year 1: Debt is 2 million. Interest is 0.12 * 2 million = 0.24 million.
- Year 2: New debt is 2 million + 0.24 million interest from Year 1 = 2.24 million. Now calculate interest for Year 2.
- This pattern continues for 10 years, with each year adding a new debt of 2 million plus the compounded interest from the previous year's debt.
To accurately compute the value of the accumulated debt in 10 years, one would typically use a financial calculator or spreadsheet, compounding the interest annually and summing the total debt accumulated.