Determine the interest earned for a 23-year investment with an interest rate of 2.8% compounded daily, if the Future Value is $44800
A) 21 271.02 B) 208.60 C) 20 955.11 D) 20 409.95
Here we do not know the initial investment, P.
We can still apply the formula to solve for it since we know the future value = $44800.
From
FV=44800=P(1+0.028/365)^(23*365)
we solve for P
P=44800/((1+0.028/365)^(23*365))
=23528.98
The interest earned is therefore
FV-PV=$21271.02
Note: since it is daily interest, the number of days in a year can be important, considering leap years. To calculate to that precision, we need to know from which year to which year, hence the number of leap years. However, the difference will be much less than one cent, so it does not really make a difference for this problem.
To determine the interest earned for a 23-year investment with an interest rate of 2.8% compounded daily, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value
P is the principal amount
r is the annual interest rate (as a decimal)
n is the number of times that interest is compounded per year
t is the number of years
In this case, the future value (A) is given as $44,800. The principal amount (P) is not given. We need to solve for P. Let's rearrange the formula:
P = A / (1 + r/n)^(nt)
Now we can substitute the given values into the formula:
P = $44,800 / (1 + 0.028/365)^(365*23)
P ≈ $19,954.89
The principal amount is approximately $19,954.89. To find the interest earned, subtract the principal amount from the future value:
Interest earned = $44,800 - $19,954.89
Interest earned ≈ $24,845.11
So, the correct option is C) $20,955.11.