Future Value Calculation in Investment Funds

What is the accumulated value of a 100 investment at time 4?

Given an investment of 1200 into a fund at time 0, the fund develops the following balances over the next four years. If 100 is invested at time 1, under the same interest rate environment, find the accumulated value of the 100 at time 4 to the nearest cent.

Answer:

After doing calculations based on the data given in the question, the accumulated value of the 100 at time 4 is 121.55.

We can use the formula for future value of a single sum to calculate the accumulated value of the 100 at time 4. The formula is FV=PV x(1+i)^n, where PV is the present value, i is the interest rate, and n is the number of periods.

In this case, the present value is 100, the interest rate is 5%, and the number of periods is 3 (since we are calculating the accumulated value at time 4, which is 3 years after time 1). Plugging these values into the formula, we get FV = 100 x (1 + 0.05)^3 = 121.55.

What is the accumulated value at the end of year 4 for an investment of 2000 at the beginning of year 3?

Given a fund with the following effective rates: i = 0.05 and i = 0.035, what is the accumulated value at the end of year 4 for 2,000 invested in this fund at the beginning of year 3 (time = 2)? (nearest cent)

Answer:

The accumulated value at the end of year 4 for 2,000 invested in the fund at the beginning of year 3 is 2,261.78.

We can use the formula for future value of a single sum to calculate the accumulated value of the 2,000 at the end of year 4. The formula is FV = PV x (1 + i)^n, where PV is the present value, i is the interest rate, and n is the number of periods.

In this case, the present value is 2,000, the interest rate is 3.5%, and the number of periods is 2 (since we are calculating the accumulated value at the end of year 4, which is 2 years after the beginning of year 3). Plugging these values into the formula, we get FV = 2,000 x (1 + 0.035)^2 = 2,261.78.