Question

A young couple wants to have a college fund that will pay $25,000 at the end of each half-year for 8 years.

(a) If they can invest at 6%, compounded semiannually, how much do they need to invest at the end of each 6-month period for the next 18 years to begin making their college withdrawals 6 months after their last investment? (Round your answer to the nearest cent.)

A young couple wants to have a college fund that will pay $25,000 at the end of each half-year for 8 years.

(b) Suppose 8 years after beginning the annuity payments, they receive an inheritance of $37,000 that they contribute to the account, and they continue to make their regular payments as found in part (a). How many college withdrawals will they be able to make before the account balance is $0? (Round your answer to the nearest whole number.)

Answer 1

	(a)
	STEP1	Amount required at the end of 18 years
	Rate	Semi annual interest rate(6/2)	3%
	Pmt	Semi annual withdrawal amount	$25,000
	Nper	Number of semi annual withdrawals	16	(8*2)
	PV	Amount Required at the end of 18 years from today	$314,027.55	(Using PV function of excel with Rate=3%, Nper=16, Pmt=-25000)
		(Present Value of withdrawals)
	STEP 2	Semi annual Savings Required to accumulate $314027.55 at the end of 18 years
	Fv	Future Value of savings required	$314,027.55
	Rate	Semi annual interest rate(6/2)	3%
	Nper	Number of semi annual installment saved	36	(18*2)
	PMT	Savings required every six months period	$14,383.65	(Using PMT function of excel with Rate=3%, Nper=36, Fv=-314027.55)
	(b)
	PV	Amount of inheritance received	$37,000
	Rate	Semi annual interest rate	3%
	Pmt	Amount of semi annual withdrawals	$25,000
	NPER	Number of college withdrawals , they can make	1.536458181	(Using NPER function of excel with Rate=3%, Pmt=25000, Pv=-37000)
											Clipboard Font Alignment 5 Number 5 Styles D9 - X face =PV(D6, D8,-07) A B D E F G H I J K L (a) STEP1 Amount required at the end of 18 years Rate Pmt Nper $25,000 16 (8*2) Semi annual interest rate(6/2) Semi annual withdrawal amount Number of semi annual withdrawals Amount Required at the end of 18 years from today (Present Value of withdrawals) PV $314,027.55 (Using PV function of excel with Rate=3%, Nper=16, Pmt=-25000) Clipboard Font Alignment Number Styles Cells D17 - X fic =PMT(D15,016,-014) F G H I J K L AB Rate Semi annual interest rate(6/2) Pmt Semi annual withdrawal amount Nper Number of semi annual withdrawals Amount Required at the end of 18 years from PV today (Present Value of withdrawals) D E 3% $25,000 16 (8*2) $314,027.55 (Using PV function of excel with Rate=3%, Nper=16, Pmt=-25000) STEP 2 Semi annual Savings Required to accumulate $314027.55 at the end of 18 years Future Value of savings required Semi annual interest rate(6/2) Number of semi annual installment saved Savings required every six months period $314,027.55 3% 36 (18*2) $14,383.65! (Using PMT function of excel with Rate=3%, Nper=36, Fv=-314027.55) Nper Clipboard S Font Alignment Number Styles Cells D23 -: * f =NPER(D21,022,-D20) A B E F G H I J K (Present Value of withdrawals) STEP 2 Semi annual Savings Required to accumulate $314027.55 at the end of 18 years Fv Future Value of savings required Semi annual interest rate(6/2) Number of semi annual installment saved Savings required every six months period $314,027.55 3% 36 (18*2) $14,383.65 (Using PMT function of excel with Rate=3%, Nper=36, Fv=-314027.55) Nper PMT (b) PV Rate Pmt NPER Amount of inheritance received $37,000 Semi annual interest rate 3% Amount of semi annual withdrawals $25,000 Number of college withdrawals, they can make 1.536458181! (Using NPER function of excel with Rate=3%, Pmt=25000, Pv=-37000)