Question

What amount must be invested today at an interest rate of 5. 5% compounded monthly, if you want to purchase a $550,000 machine 5 years in future?

Answer 1

The amount that needs to be invested today at an interest rate of 5. 5% is determined to be $ 420,824.

Interest rate:

• A fee charged by a lender to a borrower known as an interest rate is computed as a percentage of the principal, or the loaned amount. The annual percentage rate, or APR, is typically used to express the interest rate on a loan (APR).
• Given, Future value of the car F=$ 550,000
• Rate of interest (i) =5.5% per annum Interest time periods (n)=5 years.
• PART 1:In the provided problem, the future worth of an automobile, the interest rate, and the length of the investment are all predetermined.
• Calculating the amount that must be invested now in order to obtain cash equivalent to the car's future value at the conclusion of the investment period is required.
• For this purpose, we will need to apply the PRESENT WORTH COMPUND AMOUNT FACTOR (PWCAF). This factor can be expressed as: P W C A F=$\left(\frac{P}{F}, i, n\right)=\frac{1}{(1+i)^{n}}$
• PART 2:The total amount that needs to be invested today can be computed as: P=P W C A $\times F=\frac{F}{(1+i)^{n}}$
• P=$\frac{550000}{(1+5.5 \%)^{5}}$
• P=420824 [Rounded off to whole dollars]
• Thus, the amount that needs to be invested today is determined to be:  $ 420,824

Learn more about interest rate here brainly.com/question/25793394

#SPJ4