Respuesta :
Compound interest is the interest on a particular sum of money that is compounded over a certain period of time.
It will take Ivan 5.42 years to have enough money for his project assuming he made no withdrawals.
From the question, we are asked to find "how long", which means we are to find the time "t".
The formula to find time for an interest that is compounded monthly is given as:
t = ln(A/P) / n[ln(1 + r/n)]
Where:
A = Amount after "t" years = $3580
P = Principal = Initial amount invested = $2000
n = Number of times interest is compounded = Monthly = 12 times
R = Interest rate = 10.8%
- First, convert R as a percent to r as a decimal
r = R/100
r = 10.8/100
r = 0.108 per year,
- Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(3580/2000) / ( 12 × [ln(1 + 0.108/12)] )
t = ln(3580/2000) / ( 12 × [ln(1 + 0.009)] )
t = 5.415 years
Approximately, to the nearest hundredth: 5.42 years.
Therefore, it will take Ivan 5.42 years to have enough money for his project assuming he made no withdrawals.
To learn more, visit the link below:
https://brainly.com/question/24277782
