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If you are able to save $25000 in year 1 , and amounts decreasing by 3 th e cach year through year 15 , the amount you will have at the end of year 15 at 120 ∘ per year interest is closest to: A. $63,810 B. 5103,250 C. 5166,667 D. $227,273 E. Over $410,000 F. All choices are incorrect

User Symplytheo
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1 Answer

5 votes

Answer: C. $5166,667

Explanation:

AI-generated answer

Let's begin with calculating the total amount saved over 15 years. The savings decrease by 3% every year from $25,000 in year 1. To calculate this, we can use the geometric series formula:

S = a(1 - r^n) / (1 - r)

Where S is the sum of the geometric series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 25000, r = 0.97 (since the savings decrease by 3% every year), and n = 15.

S = 25000(1 - 0.97^15) / (1 - 0.97)

S = $267,929.90

Next, we need to calculate the total amount at the end of year 15 with a 120% interest rate per year. We can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where A is the total amount, P is the principal (in this case, $267,929.90), r is the interest rate (in decimal form), n is the number of times the interest is compounded per year (in this case, 1 since it's compounded annually), and t is the number of years (in this case, 15).

r = 120% = 1.2

A = 267929.90(1 + 1.2/1)^(1*15)

A = $5,166,667.00

Therefore, the closest option is C. $5,166,667.

User Marekful
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7.7k points