A person has an amount of € 10 000 which he wants to use as a provision for old age. He decides to invest 20% of his money in an equity fund (or stock fund) and 80% in a bond fund. It is more risky to invest your money in an equity fund than in a bond fund, but in the long run equity funds have a greater return than bond funds. Assume that the money invested in the equity fund grows by 8% per year and that the money invested in the bond fund grows by 4% per year. Denote the money in the equity fund by S and the money in the bond fund by B. Both depend on the time t, which we measure in years and such that t = 0 corresponds to the moment in time when the person starts his investment. a. How long does it take the money in the equity fund to double in value? b. At the time the person starts his investment, the money in the equity fund is 20% of the total capital. What percentage of the total capital is in the equity fund after 5 years? c. Write an equation that gives the percentage F for the total capital that is in the equity fund after t years.
1 A person has an amount of € 10 000 which he wants to use as a provision for old age. He decides to invest 20% of his money in an equity fund (or stock fund) and 80% in a bond fund. It is more risky to invest your money in an equity fund than in a bond fund, but in the long run equity funds have a greater return than bond funds. Assume that the money invested in the equity fund grows by 8% per year and that the money invested in the bond fund grows by 4% per year. Denote the money in the equity fund by S and the money in the bond fund by B. Both depend on the time t, which we measure in years and such that t = 0 corresponds to the moment in time when the person starts his investment.
a. How long does it take the money in the equity fund to double in value?
b. At the time the person starts his investment, the money in the equity fund is 20% of the total capital. What percentage of the total capital is in the equity fund after 5 years?
c. Write an equation that gives the percentage F for the total capital that is in the equity fund after t years.
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