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 $10,000 in an account for 5 yr for which the interest is compounded monthly. 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 = 4.0 % b. r = 6.0 % c. r = 8.0 % d. r = 9.5 %
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 $10,000 in an account for 5 yr for which the interest is compounded monthly. 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 = 4.0 % b. r = 6.0 % c. r = 8.0 % d. r = 9.5 %
Solution Summary: The author calculates the amount of money in the account after 5 years if compounded monthly for 10,000 invested at 4%.
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 $10,000 in an account for 5 yr for which the interest is compounded monthly. 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
=
4.0
%
b.
r
=
6.0
%
c.
r
=
8.0
%
d.
r
=
9.5
%
Jamal wants to save $48,000 for a down payment on a home. How much will he need to invest in an
account with 11.8% APR, compounding daily, in order to reach his goal in 10 years? Round to the
nearest dollar.
r
nt
Use the compound interest formula, A (t) = P(1 + 1)".
An account is opened with an intial deposit of $7,500 and earns 3.8% interest compounded semi-
annually. Round all answers to the nearest dollar.
a. What will the account be worth in 10 years? $
b. What if the interest were compounding monthly? $
c. What if the interest were compounded daily (assume 365 days in a year)? $
Kyoko has $10,000 that she wants to invest. Her bank has several accounts to choose from. Her goal is
to have $15,000 by the time she finishes graduate school in 7 years. To the nearest hundredth of a
percent, what should her minimum annual interest rate be in order to reach her goal assuming they
compound daily? (Hint: solve the compound interest formula for the intrerest rate. Also, assume there
are 365 days in a year)
%
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