How many days will it take for a sum of $2000 to earn $40 interest if it is deposited in a bank paying simple interest at the rate of 3.6% per year?
What I did:
I=Prt
40=2000(3.6t)
40=7200t
40/7200=7200t/7200
t= .0055555556
In general, the formula I=Prt
has I in dollars
P in dollars
r : then annual interest year, expressed as a decimal
t: the time in years.
so:
40 = 2000(.036)t
t = 40/(2000(.036)) = .5555... or 5/9 years
to convert that to days, we have to multiply it by 365
so t = (5/9)(365) or 202.777. or appr 203 days
check:
P = 2000
r = .036
t = 203/365
I = 2000(.036)(203/365) = 40.04 , 4 cents off because we rounded to the nearest day
I = P*r*T.
40 = 2000*(0.036/365)*T.
40 = 0.1973T,
T = 203 Days.
To calculate the number of days it will take for a sum of $2000 to earn $40 interest at a rate of 3.6% per year, we need to use the formula for simple interest:
I = Prt
Where:
I = Interest earned
P = Principal (initial amount)
r = interest rate per year (as a decimal)
t = time in years
In this case, the principal is $2000, the interest rate is 3.6% (or 0.036 as a decimal), and we need to find how many days it takes to earn $40, so the interest earned (I) is $40.
Let's substitute these values into the formula and solve for t:
40 = 2000 * 0.036 * t
Simplifying:
40 = 72t
Divide both sides of the equation by 72:
40/72 = t
0.555555556 = t
To convert the time from years to days, we need to multiply t by 365 (assuming a year has 365 days):
0.555555556 * 365 = 202.77777778
Therefore, it will take approximately 203 days for a sum of $2000 to earn $40 interest at an interest rate of 3.6% per year.