Question

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Problem #8: An initial deposit of $7500 1s made nto an account now, and a second deposit of $18000 1s made înto the same account after 15 years. During the first 10 years, the account earns interest quoted at a nominal quarterly discount rate of d%. After 10 years have passed, any money in the account earns a nominal semi-annual interest rate of 6.4%. At the end of 30 years, the total value of the account will be $1 16 173, what is the value of d (to the nearest 0.1%)? d as a percentage, correct to 1 decimal Problem #8: Just Save Your work has been saved! (Back to Admin Page) Submit Problem #8 for Grading Problem #8| Attempt #1 Your Answer: Attempt #2 Attempt #3 | Attempt #4 Attempt #5 Your Mark:

Answer 1

A	B	C	D	E	F	G	H	I
2
3		The future value in the account can be calculated as follows:
4
5		Future value for $7500 deposited at Year0	=7500*(1+d/4)(10*4)*(1+6.4%/2)(20*2)
6			=26439.25*(1+d/4)40
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8		Future value for $18,000 deposited at Year 15	=18,000*(1+6.4%/2)(15*2)
9			$46,308.79	=18000*((1+6.4%/2)^(15*2))
10
11		Total Future Value at year 30	=$46,308.79 + 26439.25*(1+d/4)40
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13		Given the future value	$116,173
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15		Equation can be written as
16		$116,173=$46,308.79 + 26439.25*(1+d/4)40
17
18		Solving the above equation
19		d	9.8%	=4*((((D13-D9)/26439.25)^(1/40))-1)
20
21		Hence Value of d is	9.8%
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