Question

Chase has nothing saved for college. He will need to pay 22,480 dollars per year to the school for 5 years. The first of these payments will be made in 6 years. Chase can earn 10.08 percent per year. How much does Chase need to save each year for 5 years to have exactly enough to pay for his education if he makes his first savings contribution later today and all savings contributions are equal? Chase also has nothing saved for retirement. He wants to receive 65,600 dollars each year for 8 years during retirement. The first of these payments will be received in 3 years. Chase can earn a return of 10.61 percent per year. How much does Chase need to save each year for 3 years to have exactly enough to meet his retirement goal if he makes his first savings contribution in 1 year and all savings contributions are equal? Chase also plans to save 12,900 dollars per year for 3 years. His first savings contribution is expected later today. He then plans to make withdrawals for 3 years. How much can Chase expect to withdraw each year if he expects to earn 8.55 percent per year, he makes equal annual withdrawals, and his first withdrawal is made in 4 years?

Answer 1

Solution :-

(i) Interest Rate = 10.08% Per Year

College fees per year = $22,480

Present Value of College fees at Year 5 = Future Value of Savings at Year 5

Now assume Savings per year be X

$22,480 * PVAF ( 10.08% , 5 ) = X * FVAF ( 10.08% , 5 ) * FVF ( 10.08% , 5 )

( $22,480 * 3.783 ) = ( X * 6.1148 ) * ( 1 + 0.1008 )

X = $12,634.03

Therefore Annual Savings made = $12,634.03

(ii)

Present Value of Amount receive after Retirement = $65,600 * PVAF ( 10.61% , 8 ) * PVF ( 10.61% , 2 )

= $65,600 * 5.21849 * 0.8174

= $279,80.73

Now let the amount of annual Saving be X

Now Present Value today of 3 Years Deposit

= X * PVAF ( 10.61% , 3 )

= X * 2.4604

Now Take these two equal to Find annual Deposit

= X * 2.4604 = $279,80.73

X = $113,725.12

(iii)

Present Value of Savings = $12,900 * PVAF ( 8.55% , 3 )

= $12,900 * 2.5517

= $32,917.37

Now Assume the Value of Withdrawal be X

Now Present Value of Withdrawals = X * PVAF ( 8.55% , 3 ) * PVF ( 8.55% , 3 )

= X * 2.55174 * 0.7818

= X * 1.995

Now Equate both to get Value of X

= X * 1.995 = $32,917.37

X = $16,500

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