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Three years from now, Jane will deposit the first of eight payments into a specialised
investment fund offered by her local credit union. The fund will earn interest at a rate
of 5 percent per year until the third deposit is made. Afterwards, the fund will return a
reduced interest rate of 4 percent compounded annually until the final deposit is made.
Construct the timeline. How much money will the investor have in this investment
vehicle at the end of ten years assuming no withdrawals?

Sagot :

The value at 10 years given an interest rate of 5% in 3 years and 4% in

the 7 years is 10.007 times one of the annual payments.

Which method can be used to calculate the future value of the investment?

Interest in the first year = 5% = 0.05

Let P represent the annual payments

The amount in the investment are as follows;

In the first three years are;

Amount at the start of the 1st year = P

Amount at the start of the 2nd year = P + P + (0.05·P) = 2.05·P

Amount at the start of the 3rd year = P + 2.05·P + 2.05·P × 0.05 = 3.1525·P

After the 5 years of equal payment, we have;

The future value

[tex]FV =\mathbf{3.1525\cdot P \times (1+0.04)^5 + P \times \left[\dfrac{(1 + 0.04)^5 - 1}{0.04} \right]}= 9.252 \cdot P[/tex]

At 10 years, we have;

[tex]Value \ of \ investment = 9.252 \cdot P \times (1 + 0.04)^2 \approx \underline{10.007 \cdot P}[/tex]

Learn more about the future value of an investment here:

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