Respuesta :
Answer:
Jessica will have more money after 30 years of age.
Step-by-step explanation:
It gives an annual interest rate of 6%.
So, 0.5% will be the monthly interest rate.
Now, Jessica started saving $50 per month when he turned 18 at the monthly interest rate of 0.5% and finally after she reaches 30, the total savings will be
= [tex]50(1 + \frac{0.5 \times 144}{100}) + 50(1 + \frac{0.5 \times 143}{100} + .......... + 50(1 + 0)[/tex]
= [tex]50 \times 145 + 0.25(144 + 143 + 142 + ......... + 1)[/tex]
= [tex]7250 + 0.25 \times \frac{1}{2} \times 144 \times 145[/tex]
= 9860 dollars.
Now, Beth started saving $100 per month when he turned 24 at the monthly interest rate of 0.5% and finally after she reaches 30, the total savings will be
= [tex]100(1 + \frac{0.5 \times 72}{100}) + 100(1 + \frac{0.5 \times 71}{100} + .......... + 100(1 + 0)[/tex]
= [tex]100 \times 73 + 0.5(72 + 71 + 70 + ......... + 1)[/tex]
= [tex]7300 + 0.5 \times \frac{1}{2} \times 72 \times 73[/tex]
= 8614 dollars.
Therefore, Jessica will have more money after 30 years of age. (Answer)
