1. How long will it take to triple your investment if you are earning a simple interest 5 percent annually?
a) 12.5 years b) 15 years c) 20 years d) 40 years
2. If the interest rate per compounding period is 2.3% and the annual interest rate is 9% what is the compounding frequency.
a) annually b) semi annually c) quarterly d)monthly
how do i solve these.
(1+.05n) = 3
you are adding 1/20 of the principal each year, so it will take 40 years to add twice the original amount.
9/2.3 = 3.9
That is, the 9% is divided into 3.9 equal parts.
so, quarterly
1. Po + Po*0.05*T = 3Po.
Divide both sides by Po:
1 + 0.05T = 3,
T = 40 yrs.
To solve these questions, you need to understand the formulas and concepts related to simple interest and compound interest.
1. Simple Interest:
To calculate the time it takes to triple your investment using simple interest, you can use the formula:
Time = (A / P) / R
Where:
A = final amount (triple the initial investment)
P = initial investment
R = interest rate per period
In this case, we want to calculate the time it takes to triple the investment, so A = 3P. The interest rate per period is given as 5%, or 0.05.
Using the formula, we have:
Time = (3P / P) / 0.05 = (3 / 0.05) = 60.
So, it will take 60 years to triple your investment with a simple interest rate of 5% annually.
Looking at the answer options:
a) 12.5 years
b) 15 years
c) 20 years
d) 40 years
None of the provided answer options match the calculated time. So, none of the given options is correct.
2. Compound Interest:
To find the compounding frequency, we need to know the relationship between the interest rate per compounding period and the annual interest rate.
The formula to calculate the future value of an investment with compound interest is:
FV = P(1 + r/n)^(n*t)
Where:
FV = future value
P = initial investment
r = interest rate per period
n = number of compounding periods per year
t = number of years
In this case, we know that r = 2.3% and the annual interest rate is 9%. To find the compounding frequency, we need to determine the value of n.
By rearranging the formula, we can solve for n:
n = (ln(1 + r)) / (ln(1 + (R/n)) - where ln represents the natural logarithm and R is the annual interest rate.
Simplifying the equation, we get:
n = (ln(1 + r)) / (ln(1 + (0.09/n)))
Now, let's calculate the compounding frequency using the given values:
n = (ln(1 + 0.023)) / (ln(1 + (0.09/n))) = (0.0227) / (0.0909/n)
We can simplify this further by dividing both sides by 0.0227:
1/n = 0.0909 / 0.0227
Calculating the right-hand side, we have:
1/n = 3.999
Now, taking the reciprocal of both sides, we get:
n = 1/3.999 = 0.25
Therefore, the compounding frequency is quarterly.
Now, let's look at the answer options:
a) annually
b) semi-annually
c) quarterly
d) monthly
The correct answer is c) quarterly, as we found that the compounding frequency is quarterly.