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.