Can someone please just give me the right answer to the right decimal places for the last part, "How much interest was earned during the third quarter of the 4th year?" I've received more than 5 wrong answers already.  A corporation creates a sinking fund in order to have $860,000 to replace some machinery in 11 years. How much should be placed in this account at the end of each quarterif the annual interest rate is 6.5% compounded quarterly? (Round your answers to the nearest cent.)$ How much interest would they earn over the life of the account?$264439.07 $

Question
Asked Oct 23, 2019

Can someone please just give me the right answer to the right decimal places for the last part, "How much interest was earned during the third quarter of the 4th year?" I've received more than 5 wrong answers already. 

 

A corporation creates a sinking fund in order to have $860,000 to replace some machinery in 11 years. How much should be placed in this account at the end of each quarterif the annual interest rate is 6.5% compounded quarterly? (Round your answers to the nearest cent.)
$

How much interest would they earn over the life of the account?
$264439.07
$

check_circleExpert Solution
Step 1

It is given that,

Required accumulated amount is $860,000.

Number of years is 11. So, total number of payments will be (11 × 4) = 44.

Interest rate is 6.5% compounded quarterly. So, interest rate per quarter will be (6.5% ÷ 4) = 1.625%.

Step 2

The quarterly amount to be deposited is calculated below:

(1+1)-1
Accumulated value = Quarterly paymentx
i
4
(1+1.625%)
-1
$860,000 Quarterly paymentx
1.625%
1.032472
$860,000 Quarterly paymentx
0.01625
$860,000 Quarterly payment x 63.536738
$860,000
= Quarterly payment
63.536738
$13,535.476 Quarterly payment
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(1+1)-1 Accumulated value = Quarterly paymentx i 4 (1+1.625%) -1 $860,000 Quarterly paymentx 1.625% 1.032472 $860,000 Quarterly paymentx 0.01625 $860,000 Quarterly payment x 63.536738 $860,000 = Quarterly payment 63.536738 $13,535.476 Quarterly payment

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Step 3

The total amount paid by the corporation will be ($13,535.476 × 44) = $595,560...

Interest earned Accumulated value - Total amount paid
$860,000-$595,560.944
= $264, 439.05
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Interest earned Accumulated value - Total amount paid $860,000-$595,560.944 = $264, 439.05

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