Question

PART 1

1. Aunt Esmeralda promises to give her nephew $35,000 on his 30th birthday, 14½ years from now. Aunt Esmeralda can earn 5.8% compounded semiannually. What amount could Aunt Esmeralda deposit today in a savings plan so that the plan would have required $35,000 in 14 1/2 years?

   		$6,823.13
   		$15,453.46
   		$23,123.05
   		$15,276.44

PART 2

Refer to Problem 1. If, instead, Aunt Esmeralda elects to make semiannual deposits into the plan (starting in 6 months), what is the required semiannual deposit?

		$1,976.09
		$1,604.92
		$786.15
		$763.99

PART 3

Refer to Problems 1 and 2. If Aunt Esmeralda deposits $5,000 today, what additional amount must she deposit at the end of each semiannual period?

		$528.84
		$14,819.76
		$1,548.79
		$1,085.64

Answer 1

PART 1

Future value	35,000.00
Period (in years)	14.5
Period (in half-years)	29
Interest rate	5.80%
Semi annual rate	2.90%

Future value = present deposit amount x Future value factor

35000 = present deposit amount x (1+semi annual rate)^no. of half years

35000 = present deposit amount x (1+2.9%)^29

35000 = present deposit amount x 2.2911

35000 / 2.2911 = present deposit amount

Present deposit amount = $ 15,276.44

Therefore the right option is $ 15,276.44

PART 2

Future value	35,000.00
Period (in years)	14.5
Period (in half-years)	29
Interest rate	5.80%
Semi annual rate	2.90%

Future value = semi annual deposits x Future value annuity factor

35000 = semi annual deposits x (((1+semi annual rate)^no.of half years -1)/semi annual rate)

35000 = semi annual deposits x (((1+2.9%)^29-1)/2.9%)

35000 = semi annual deposits x 44.5210

35000 / 44.5210 = semi annual deposits

semi annual deposits = $ 786.15

Therefore the right option is $ 786.15

PART 3

Future value	35,000.00
Present deposit	5,000.00
Period (in years)	14.5
Period (in half-years)	29
Interest rate	5.80%
Semi annual rate	2.90%

Future value = (Present deposit x FV factor ) + (semi annual deposits x Future value annuity factor)

35000 = (Present deposit x (1+semi annual rate)^no. of half years) + (semi annual deposits x (((1+semi annual rate)^no.of half years -1)/semi annual rate))

35000 = (5000 x (1+2.9%)^20) + (semi annual deposits x ((((1+2.9%)^29) -1)/2.9%))

35000 = (5000 x 2.2911 )+ (semi annual deposits x 44.5210)

35000 = 11455.55 + (semi annual deposits x 44.5210)

35000 - 11455.55 = (semi annual deposits x 44.5210)

23544.45 = (semi annual deposits x 44.5210)

23544.45 /44.5210 = semi annual deposits

Semi annual deposits = 528.84

Therefore the right option is $ 528.84

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