Final Answer:
The couple would have approximately $382,107.60 in the account at the end of the 30-year period.
Explanation:
Initially, the couple intended to take a 30-year loan of $100,000 at a 9 3/4% annual interest rate, compounded monthly, for purchasing a house. If they were to make the monthly payments into an account yielding the same interest rate compounded monthly instead of opting for the loan, the account would accumulate around $382,107.60 over the 30-year span.
By choosing the loan, they would have been committed to monthly payments for 30 years, amounting to a total payment of $329,427.04. However, by redirecting these monthly payments into an account that accrues interest at the same rate, compounded monthly, they would be essentially saving these payments and allowing them to compound. This strategy would result in significant growth due to compounded interest over the same period.
The magic of compounding interest lies in the snowball effect, where the initial amount, combined with subsequent contributions, grows substantially over time. In this case, the consistent monthly deposits, coupled with the compounded interest, generate a substantial balance at the end of the 30-year period. This amount significantly surpasses the original loan payment and showcases the power of compound interest when used strategically over an extended period.
Choosing the investment route, in this scenario, showcases the potential of disciplined, consistent saving coupled with compounding interest. It highlights the advantage of investing and allowing money to grow over time, enabling individuals to potentially secure a more substantial financial future compared to committing to a long-term loan obligation.