Question

Deposit $150 at the end of every month for ten years into a savings account that earns 3% compounded monthly. at the end of the ten years, transfer the accumulated money into an investment fund that earns 6% compounded quarterly, and allow the money to grow in this fund until retirement. long (in years and months) would it take to accumulate the required amount of $45,000 to pay for his vacation? ensure that the amount accumulates to only $45,000 at the time of retirement, by how much should he change his monthly deposit?

A) It will take 13 years and 8 months. He should increase his monthly deposit to $180.
B) It will take 15 years and 2 months. He should decrease his monthly deposit to $120.
C) It will take 12 years and 4 months. He should increase his monthly deposit to $175.
D) It will take 14 years and 6 months. He should decrease his monthly deposit to $130.

Answer 1

The question requires complex financial calculations involving annuities and lump sums, but lacks sufficient details to provide an accurate answer regarding the time required to accumulate $45,000 or the necessary adjustment to monthly deposits.

Step-by-step explanation:

The student's question involves calculating the future value of regular savings deposits and then determining how long it would take for an investment to grow to a specific amount. This falls under the subject of financial mathematics, a branch of applied mathematics. It requires understanding of the future value of an annuity formula for the savings account scenario and the future value of a lump sum for the investment fund scenario. However, to properly assist the student, it would be necessary to perform calculations using both the future value of an annuity formula (for the monthly deposits) and the future value of a lump sum formula (for the growth after transferring to the investment fund). Unfortunately, the question doesn't provide clear information about the period of time between the end of the ten-year savings and the retirement, nor does it give us the initial amount needed to check against the options provided (A, B, C, and D). Thus, due to insufficient and ambiguous information, I am unable to accurately calculate and answer the student's question.