For Exercises 11–16, suppose that P dollars in principal is invested at an annual interest rate r . For interest compounded n times per year, the amount A ( t ) in the account after t years is given by A ( t ) = P ( 1 + r n ) n t . If interest is compounded continuously, the amount is given by A ( t ) = P e r t . Suppose an investor deposits $5000 in an account for 8 yr for which the interest is compounded quarterly. Find the total amount of money in the account for the following interest rates. Compare your answers and comment on the effect of interest rate on an investment. a. r = 4.5 % b. r = 5.5 % c. r = 7.0 % d. r = 9.0 %
For Exercises 11–16, suppose that P dollars in principal is invested at an annual interest rate r . For interest compounded n times per year, the amount A ( t ) in the account after t years is given by A ( t ) = P ( 1 + r n ) n t . If interest is compounded continuously, the amount is given by A ( t ) = P e r t . Suppose an investor deposits $5000 in an account for 8 yr for which the interest is compounded quarterly. Find the total amount of money in the account for the following interest rates. Compare your answers and comment on the effect of interest rate on an investment. a. r = 4.5 % b. r = 5.5 % c. r = 7.0 % d. r = 9.0 %
Solution Summary: The author calculates the total amount of money in the account after 8 years if compounded quarterly for 5000 invested at 4.5%.
For Exercises 11–16, suppose that P dollars in principal is invested at an annual interest rate r. For interest compounded n times per year, the amount
A
(
t
)
in the account after t years is given by
A
(
t
)
=
P
(
1
+
r
n
)
n
t
. If interest is compounded continuously, the amount is given by
A
(
t
)
=
P
e
r
t
.
Suppose an investor deposits $5000 in an account for 8 yr for which the interest is compounded quarterly. Find the total amount of money in the account for the following interest rates. Compare your answers and comment on the effect of interest rate on an investment.
a.
r
=
4.5
%
b.
r
=
5.5
%
c.
r
=
7.0
%
d.
r
=
9.0
%
Suppose that $71,000 is invested at 3 & a 1/2% interest, compounded quarterly.
a) Find the function for the amount to which the investment grows after t years.
b) Find the amount of money in the account at t=0, 4, 6, and 10 years.
An investment grows according to the formula,where t is time, measured in months.
When a particular amount of money P, called the principal, is invested at the interest rate r and is compounded
n times a year, the amount A accumulated after t
years
is
A(t) – P(1+ )".
= P(1-+
n
Determine the amount of money accumulated after 15 years if $5,000 is invested in an account that pays 10 %
interest compounded yearly. Round to the nearest cent.
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