Final answer:
To calculate Tanzania's accumulated debt after 10 years of financing a consistent budget gap of 2 million shillings by issuing 12% interest bonds, one needs to account for the compound interest on the yearly shortfall turned debt.
Step-by-step explanation:
The question revolves around the computation of accumulated debt for a government that has decided to finance a budget deficit through the issuance of bonds. The challenge is to compute the value of the debt after 10 years, given the government of Tanzania's spending and revenue measures. The government plans to spend 10 million shillings annually on schools, roads, and healthcare and expects to collect 8 million shillings in net taxes, leaving a shortfall of 2 million shillings. The shortfall is financed by selling 10-year government bonds with a 12% interest rate. Each year, the government raises additional taxes to cover the interest expense, ensuring that the budget shortfall remains consistent at 2 million shillings.
To compute the accumulated debt over 10 years, we must take into account not only the annual shortfall but also the compounding interest on the bonds issued each year. In the first year, the debt is simply the 2 million shilling shortfall. In the second year, the new debt is 2 million shillings plus the interest on the previous year's debt, and so on. As the government raises taxes to cover the growing interest expenditure, the original 2 million shilling gap remains constant, but the actual debt grows as interest accumulates on the bonds.
By using the formula for the future value of an annuity with compound interest, we can calculate the future value of the government's debt, factoring in the interest accruing annually. This requires iterative calculations for each year's new debt, plus the accumulated interest on past debt until the 10th year, at which point we can determine the total debt accumulated.