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2 votes
Natalia Sanchez can invest $20,000 at either 4.5% compounded daily for 4 yes

compounded monthly for 4 years. Based on an annual percentage yield, which is
better investment?

User Wlyles
by
8.4k points

2 Answers

1 vote

Final answer:

To decide which investment option is better for Natalia Sanchez, we will calculate the future value of $20,000 compounded daily versus monthly at 4.5% interest rate over 4 years and compare the results.

Step-by-step explanation:

To determine which investment Natalia Sanchez should choose based on annual percentage yield (APY), we need to calculate the compound interest for both scenarios: compounded daily and compounded monthly for $20,000 over 4 years.

Compound interest formula is A = P(1+r/n)^(nt).

Where:

A = the amount of money accumulated after n years, including interest.

P = the principal amount (the initial amount of money).

r = the annual interest rate (decimal).

n = the number of times that interest is compounded per year.

t = the time in years.

For daily compounding:
A = $20,000(1 + 0.045/365)^(365*4).

For monthly compounding:
A = $20,000(1 + 0.045/12)^(12*4).

Calculate both A values and compare to see which one is higher. The one with the higher A value represents the better investment based on APY.

User Anjoe
by
8.8k points
5 votes

Answer:

compounded daily

Step-by-step explanation:

20000×(1+(
(0.045)/(365))³⁶⁵ˣ⁴= $2394.41

20000×(1+(
(0.045)/(12))¹²ˣ⁴= $2393.63

User Tho Ho
by
8.4k points

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