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12.Larry decide to begin saving towards the purchase of a backup generator in 5 years. If...

12.Larry decide to begin saving towards the purchase of a backup generator in 5 years. If he puts $2,000 at the beginning of each of the next 5 years in a savings account paying 9 percent compounded quarterly, how much will you accumulate after 5 years? Note: You are only making 5 payments, and the first payment is today. a. $11,636.23 b. $13,046.67 c. $11,969.42 d. $12,043.17 e. $13,164.19

Expert Solution

Annual interest rate = 9%, Compounded Quarterly

Quarterly interest rate = 9%/4 = 2.25%

Effective annual interest rate = EAR = (1+2.25%)⁴ - 1 = 0.0930833187890623 = 9.30833187890623%

Larry puts 2,000 at the beginning of the next 5 years. Following table shows the cash flow in different years

time period	0	1	2	3	4	5
Deposit	2000	2000	2000	2000	2000

First cash flow occurs now [at t=0], C₁ = 2000

Future value of C₁ at [t=5 years] = C₁*(1+EAR)⁵ = 2000*(1+ 9.30833187890623%)⁵ = 3121.01840136943

2. Second cash flow occurs at [t=1], C₂ = 2000

Future value of C₂ at [t=5 years] = C₂*(1+EAR)⁴ = 2000*(1+ 9.30833187890623%)⁴ = 2855.24291490145

3. Third cash flow occurs at [t=2], C₃ = 2000

Future value of C₃ at [t=5 years] = C₃*(1+EAR)³ = 2000*(1+ 9.30833187890623%)³ = 2612.09997977513

4. Fourth cash flow occurs at [t=3], C₄ = 2000

Future value of C₄ at [t=5 years] = C₄*(1+EAR)² = 2000*(1+ 9.30833187890623%)² = 2389.66228362982

5. Fifth cash flow occurs at [t=5], C₅ = 2000

Future value of C₅ at [t=5 years] = C₅*(1+EAR)¹ = 2000*(1+9.3083% 9.30833187890623%)¹ = 2186.16663757812

Total value of the future = Fututre value of C₁ + Fututre value of C₂ + Fututre value of C₃ + Fututre value of C₄ + Fututre value of C₅ = 3121.01840136943+2855.24291490145+ 2612.09997977513 + 2389.66228362982 + 2186.16663757812 = 13164.190217254

time period	0	1	2	3	4	5
Deposit	2000	2000	2000	2000	2000
Future Value at t=5	3121.01840	2855.24291	2612.09998	2389.66228	2186.16664

Answer -> e. 13164.19

jeff jeffy answered 3 months ago

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