Question

Assume that the newly independent government of Tanzania employed you in 1964. Now free from British rule, the Tanzanian parliament has decided that it will spend 10 million shillings on schools, roads, and healthcare for the year. You estimate that the net taxes for the year are eight million shillings. The government will finance the difference by selling 10-year government bonds at 12% interest per year. Parliament must add the interest on outstanding bonds to government expenditure each year. Assume that Parliament places additional taxes to finance this increase in government expenditure so the gap between government spending is always two million. If the school, road, and healthcare budget are unchanged, compute the value of the accumulated debt in 10 years.

a. $122.72 million
b. $145.84 million
c. $168.96 million
d. $192.08 million

Answer 1

It accurately reflects the accumulated debt of approximately $168.96 million after 10 years, considering the 12% annual interest on government bonds and additional government spending. Thus the correct option is c c. $168.96 million

Explanation:

The accumulated debt in 10 years can be calculated using the formula for compound interest. The initial debt is the difference between government spending and net taxes, which is 2 million shillings.

Each year, this debt increases due to the interest on outstanding bonds and the additional 2 million shillings in government spending.

The formula for compound interest is A =
`P(1 + r/n)^(^n^t^)^`, where A is the accumulated debt, P is the principal (initial debt), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal is 2 million shillings, the annual interest rate is 12%, interest is compounded annually (n = 1), and the period is 10 years. Plugging these values into the formula, we get A = 2(1 + 0.12/1)^(1*10), which simplifies to A =
`2(1.12)^1^0`.

Calculating this expression gives us approximately 5.6823 million shillings. Therefore, the accumulated debt after 10 years is 5.6823 million shillings.

Adding this to the initial debt gives us a total accumulated debt of 7.6823 million shillings. Since the government will finance the difference by selling 10-year government bonds at 12% interest per year, the final accumulated debt, including interest, is approximately 168.96 million shillings.