Question

Your uncle offers you a choice of $115,0 in 10 years or $52,000 today, if the money is discounted at 9%, which should you do ose? 2. If you invest $9,500 per period or the fotioning number of periods how much would you have? A. 10years at 10% B. 15years at 9%

Answer 1

1) we would choose the second offer i.e. $52,000 today

2) For A) 10 years at 10%

Future value = $151,405.53

For B) 15 years at 9%

Future value = $278,928.70

Step-by-step explanation:

1) Future value = $115,000

Time, n = 10 years

Discount rate, r = 9% = 0.09

Now,

Present value of the money provided after 10 years

= Future Value ÷ [ ( 1 + r )ⁿ ]

= $115,000 ÷ [ ( 1 + 0.09 )¹⁰ ]

= $48,577.24

Since,

The Present value of $115,000 is less than the money to offered today i.e $52,000

Hence, we would choose the second offer i.e. $52,000 today

2) Payment per period = $9,500

Future value = Yearly Payment × [ { ( 1 + r ) ⁿ - 1 } ÷ r ]

Thus,

For A) 10 years at 10%

Future value = $9,500 × [ { ( 1 + 0.1 )¹⁰ - 1 } ÷ 0.1 ]

= $151,405.53

For B) 15 years at 9%

Future value = $9,500 × [ { ( 1 + 0.09 )¹⁵ - 1 } ÷ 0.09 ]

= $278,928.70