Final answer:
To find out how many years it would take for a debt to increase by 75% at a compound interest rate of 8% compounded 195 times per year, use the compound interest formula. After calculations, it takes approximately 6.6 years for the debt to grow by 75%.
Step-by-step explanation:
To determine how many years it would take for a debt to grow by 75% with an annual compound interest rate of 8% that compounds 195 times per year, you can use the formula for compound interest:
A = P(1 + r/n)nt
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time in years.
In this case, we want the debt to increase by 75%, so A will be 1.75 x P. We can then set up the equation as
1.75P = P(1 + 0.08/195)195t
Solving for t, we use logarithms:
1.75 = (1 + 0.08/195)195t
t = log(1.75) / (195 * log(1 + 0.08/195))
By calculating the above expression using a calculator, the number of years it will take for the debt to grow by 75% is approximately 6.6 years
Compound interest significantly affects the growth of money, especially over long periods and with more frequent compounding, as illustrated by the exponential growth of the invested amount over time.