To solve our problems, we are going to use the formula for compounded interest:
where
is the final amount after
years
is the initial amount
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the time in years
1. A) We know for our problem that the initial investment is $5010, so
. We also know that the interest rate is 6.4%. To express the interest in decimal form, we are going to divide it by 100%:
. Since the interest is compounded continuously, it is compounded 365 times per year; therefore,
. Lets replace those values in our formula:
We can conclude that the equation that model this situation is
B. To find the amount of money you will have after 2 years, we are going to replace
with 2 in the equation from point
A:
We can conclude that after 2 years you will have $5694.06 in your account.
2. We know for our problem that
,
, and
.
A. Since the interest is compounded quarterly, it is compounded 4 times per year; therefore,
. Lets replace the values in our formula:
We can conclude that after a year you will have $106.14 in your account.
B. Since the interest is compounded monthly, it is compounded 12 times per year; therefore,
. Lets replace the values in our formula:
We can conclude that after a year you will have $106.17 in your account.
C. Since the interest is compounded daily, it is compounded 365 times per year; therefore,
. Lets replace the values in our formula:
We can conclude that after a year you will have $106.18 in your account.
3. We know for our problem that the initial investment is $100,000, so
. We also know that the final amount will be $500,000, so
. The interest rate is 6%, so
. Since the interest rate is compunded anually, it is compounded 1 time per year; therefore,
. Lets replace the values in our formula and solve for
:
We can conclude that
is the equation to determine how long it will take before the amount in your account is $500,000
As a bonus:
We can conclude that after 27.6 years you will have $500,000 in your account.