Question

A particular savings bank pays 6% annual interest compounded continuously. How much will a deposit of $4000 amount to for each time period? Hint: Convert months to days. When needed, use 365 days per year and 30 days per month a. 6 years b. 9 years 9 months c. 4 years 11 months 24 days d. 20 years 213 days a. The amount accumulated after 6 years is $ (Round to the nearest cent as needed.) 1 b. The amount accumulated after 9 years and 9 months is $ (Round to the nearest cent as needed.) c. The amount accumulated after 4 years 11 months and 24 days is $ (Round to the nearest cent as needed.) d. The amount accumulated after 20 years 213 days is $ (Round to the nearest cont as needed.)

Answer 1

Given: The bank The bank Days 6% annual interest compounded continuousy. The formula for amount after t years is Acd= Ao est given, Ao = $4000 (initial annount) rate of interest r= 6% 20:06 :: Alt) = 4000 0.00 0. (9) 6 years putting to 6 in Ol A=4000006(6) =4000e9s6 = 4000 x 1.43333 = 5733.32 :. The amount accumutated after 6 years is $ 5733.32] (b) 9 years 9 months = 9 years + 3 years = 9+2=39 = 9.75 years. putting t=9.25 in O . A 24000 0.06 (9:75). =4000 x 1.79499098=7179.96 .. The amount accumulated after 9 years 9 months is $ 7179.96. (c) 4 years 11 months 24 dars = 4 years + 4 years + 29 years = 4.98842 years putting t= 4.9842 in 0 A24000 20:06(4.98242). 24000 x 1.3484.357=5393.74 The amount accumulated after 4 years 11 months 24 days = $5393,74 (d) 20 years 213 days = 20 yearst 13 years = 20.58356 years. putting t=20.58356 in O . A=4000 20:06 (20-58356) -4000 e 12350137 - 4000 x 3:4384256 = 13753.70 The amount accumulated after 20 years 213 days = $123753.70) =4000 e 0.585 | =4000 e 02989452.

Answer 2

SOLUTION :

For continuously compounded case, we use the following formula :

FV = A e^(r t) 

where,

FV = accumulated amount after t years.

A = amount deposited = $4000

r = rate of annual interest = 6% = 0.06

t = period of deposit in years.

a.

When t = 6 years:

FV 

= 4000 * e^(0.06 * 6) 

= 5733.32 ($) (ANSWER).

b.

When t = 9 years 9 months = 9.75 years

FV 

= 4000 * e^(0.06 * 9.75) 

= 7179.96 ($) (ANSWER).

c.

When t = 4 years 11 months 24 days = 4 + 11/12 + 24/365 = 4.98242 years

FV 

= 4000 * e^(0.06 * 4.98242) 

= 5393.74 ($) (ANSWER).

d. 

When t = 20 years 213 days = 20 + 213/365 = 20.58356 years

FV 

= 4000 * e^(0.06 * 20.58356) 

= 13753.70 ($) (ANSWER).