Question

Lee Holmes deposited $17,500 in a new savings account at 7% interest compounded semiannually. At the beginning of year 4, Lee deposits an additional $42,500 at 7% interest compounded semiannually.

At the end of 6 years, what is the balance in Lee’s account? (Use the Table provided.)

Answer 1

Annual interest of 7% means 3.5% of Semiannual interest or Effectivr interest rate is 3.5% for 6 months.

Period		Deposit balance	Addition made	Interest earned	Ending balance
Year 1	Half year	$ 17,500.00		$     612.50	$ 18,112.50
	Half year	$ 18,112.50		$     633.94	$ 18,746.44
Year 2	Half year	$ 18,746.44		$     656.13	$ 19,402.56
	Half year	$ 19,402.56		$     679.09	$ 20,081.65
Year 3	Half year	$ 20,081.65		$     702.86	$ 20,784.51
	Half year	$ 20,784.51		$     727.46	$ 21,511.97
Year 4	Half year	$ 21,511.97	$ 42,500.00	$ 2,240.42	$ 66,252.39
	Half year	$ 66,252.39		$ 2,318.83	$ 68,571.22
Year 5	Half year	$ 68,571.22		$ 2,399.99	$ 70,971.21
	Half year	$ 70,971.21		$ 2,483.99	$ 73,455.21
Year 6	Half year	$ 73,455.21		$ 2,570.93	$ 76,026.14
	Half year	$ 76,026.14		$ 2,660.91	$ 78,687.05

Interest for year 4 first half year is on $21511.97+42500

Balance of deposit at the end of Year 6 =$78,687.05

Alternate solution using Future value table.

Future value table is at interest rate of 3.5%

Deposit balance at the end of year 6
A	Initial deposit	$ 17,500.00
B	PV factor total at year 3	0.8135
C=A/B	Future value factor for 3 years	$ 21,511.99
D	Add: Additional deposit	$ 42,500.00
E=D+C	Total beginning balance of year 3	$ 64,011.99
F	Future value factor for 3 years	0.8135
G=E/F	Deposit balance at the end of year 6	$ 78,687.14

Balance of deposit at the end of Year 6 =$78,687.14

Answer by both alternative are different due round offs.

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