An investment account credits interest in such a way that a deposit of dollars made…
MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series
Problem
An investment account credits interest in such a way that a deposit of 500 dollars made at the beginning of every month immediately earns interest, but each successive month’s interest credit is only a fixed fraction r of the previous month’s credit. If the total future value of all interest credits generated by an initial 500-dollar deposit is required to be 8,000 dollars, then the financial institution must select an appropriate value of r.
(a) Formulate an equation that relates r to the total future value of 8,000 dollars.
(b) Solve the equation from part (a) to find the admissible value of r that satisfies the requirement.
(c) Verify that your solution for r guarantees convergence of the underlying infinite series of interest credits.
(d) Using the value of r found in part (b), compute the total amount of interest credited during the first 12 months and comment on how this partial total compares to the required long-run total of 8,000 dollars.