Now, let's find the future value of the annuity. Recall that the future value FV of an account after n periods where PMT payments were made at the end of each compounding period with an interest rate of i per period is FV = PMT (1+1)" - 1 The values previously determined for i and n still apply. Given that the monthly payment into the annuity is $180, PMT=83 x
Now, let's find the future value of the annuity. Recall that the future value FV of an account after n periods where PMT payments were made at the end of each compounding period with an interest rate of i per period is FV = PMT (1+1)" - 1 The values previously determined for i and n still apply. Given that the monthly payment into the annuity is $180, PMT=83 x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Find the amount accumulated FV in the given annuity account. HINT [See Quick Example 1 and Example 1.] (Assume end-of-period deposits and compounding at the same intervals as
deposits.)
Step 1
Note that this question asks us to find the amount accumulated in an annuity with an initial investment. To find the future value of the account, we will find the future value of the $15,000
and the future value of the monthly deposits separately and then find the sum of the two amounts.
Let's begin by finding the future value of the initial $15,000.
Recall that the future value FV of an investment of PV dollars earning compound interest at a rate of i per compounding period for n periods is FV =
PV(1 + i)".
$180 deposited monthly for 20 years at 3% per year in an account containing $15,000 at the start
Given that $15,000 was the initial investment, PV = 15000
If the annual interest rate of 3% per year as a decimal is 0.03, then the monthly interest rate is i =
12
Step 2
We determined that PV =
If the investment is compounded monthly for 20 years, then the number of periods of compounding is n = 12 · 20 = 240
FV =
15000
15,000, i
= 27311.32
15,000 1 +
0.03
12
27,311.32
15,000
"I
To find the future value FV, to the nearest cent, substitute the known values into the compound interest formula and proceed to simplify. (Round your final answer to the nearest cent.)
FV =
PV(1 + i)"
0.03
12
0.03
240
12
and n = 240. Now, we want to calculate the future value of the initial investment.
Thus, the future value of $15,000 at 3% per year compounded monthly for 20 years is $ 27311.32
240
27,311.32](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c73b62c-42eb-4662-ab9b-6f6c3cbd71d7%2F5ef6ed32-2ca7-4973-b76f-f9f13af58ad1%2Fp311yc_processed.png&w=3840&q=75)
Transcribed Image Text:Find the amount accumulated FV in the given annuity account. HINT [See Quick Example 1 and Example 1.] (Assume end-of-period deposits and compounding at the same intervals as
deposits.)
Step 1
Note that this question asks us to find the amount accumulated in an annuity with an initial investment. To find the future value of the account, we will find the future value of the $15,000
and the future value of the monthly deposits separately and then find the sum of the two amounts.
Let's begin by finding the future value of the initial $15,000.
Recall that the future value FV of an investment of PV dollars earning compound interest at a rate of i per compounding period for n periods is FV =
PV(1 + i)".
$180 deposited monthly for 20 years at 3% per year in an account containing $15,000 at the start
Given that $15,000 was the initial investment, PV = 15000
If the annual interest rate of 3% per year as a decimal is 0.03, then the monthly interest rate is i =
12
Step 2
We determined that PV =
If the investment is compounded monthly for 20 years, then the number of periods of compounding is n = 12 · 20 = 240
FV =
15000
15,000, i
= 27311.32
15,000 1 +
0.03
12
27,311.32
15,000
"I
To find the future value FV, to the nearest cent, substitute the known values into the compound interest formula and proceed to simplify. (Round your final answer to the nearest cent.)
FV =
PV(1 + i)"
0.03
12
0.03
240
12
and n = 240. Now, we want to calculate the future value of the initial investment.
Thus, the future value of $15,000 at 3% per year compounded monthly for 20 years is $ 27311.32
240
27,311.32
![Now, let's find the future value of the annuity.
Recall that the future value FV of an account after n periods where PMT payments were made at the end of each compounding period with an interest rate of i per period is
= 1].
FV = PMT (1 + i)^
The values previously determined for i and n still apply. Given that the monthly payment into the annuity is $180, PMT = 83
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c73b62c-42eb-4662-ab9b-6f6c3cbd71d7%2F5ef6ed32-2ca7-4973-b76f-f9f13af58ad1%2F6o8c4a_processed.png&w=3840&q=75)
Transcribed Image Text:Now, let's find the future value of the annuity.
Recall that the future value FV of an account after n periods where PMT payments were made at the end of each compounding period with an interest rate of i per period is
= 1].
FV = PMT (1 + i)^
The values previously determined for i and n still apply. Given that the monthly payment into the annuity is $180, PMT = 83
X
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