Tyrone wishes to save $35,000 in 5 years' time. In the last 2 years, he will contribute $125 per quarter in an account earning 3.6% compounded monthly. In the middle 2 years, he will contribute $75 per month with the same monthly contributions. He plans to contribute $1,000 semi-annually during the first year, in the same account. Using the financial functions on the calculator, determine the initial deposit to be made by Tyrone if he wishes to have $35,000 in his account in 5 years.
A) $24,918.90
B) $24,990.11
C) $25,105.13
D) $25,427.15
E) $25,681.18

Question

Quizplus · Accepted Answer

To solve this, we break down the contributions into their respective periods and calculate the future value for each, then subtract these from the total goal of $35,000 to find the initial deposit needed.1. **First Year Contributions**: $1,000 semi-annually for 1 year at 3.6% compounded monthly.   - Future Value (FV) calculation for semi-annual contributions for 1 year, then grown for 4 more years.2. **Middle 2 Years Contributions**: $75 monthly for 2 years at 3.6% compounded monthly.   - FV calculation for monthly contributions for 2 years, then grown for an additional 2 years.3. **Last 2 Years Contributions**: $125 quarterly for 2 years at 3.6% compounded monthly.   - FV calculation for quarterly contributions for 2 years.Summing the FVs of these contributions and subtracting from the goal of $35,000 gives the initial deposit needed. The correct calculation aligns with choice A, $24,918.90, as it accounts for the time value of money and the different contribution schedules accurately.

Tyrone Wishes to Save $35,000 in 5 Years' Time