Question

An initial deposit of $8,000 is made into an account earning 6.5% compounded continuously. Thereafter, money is deposited into the account at a constant rate of $2600 per year. Find the amount in this account at any time t. How much is in this account after 5 years? O A. A -52,000e 0.065t-44,000 $27,969.59 $26,433.47 A 44,000e 0065t-3 BA 48,000 065-40.000 $24,897.34 OD. A -60,000e 0.065t -52,000 $31,041.84

I need the solution process, thanks!

Answer 1

Solution:→ Led A be the amount afte time Amount A is changing with čespect to time t , .,th 6.6% of compound int exe st also, 2600 is added ρex yeas dA clt dA (6.5%) A t 2600 0 065A 260o dt dA clt (o-o65)A = 2600 ..。 Note: Seletion of Diffesentia Equation of tyee -0065 t -'. Solotion of (D usill be, clt -0.065 t A .65t (24c)is 3iven bg: c)Cis iven ら Ae -0.065t -0.065t = 2600 , e sedt -0.065 A6 Integ sating faictos C Integsating Now, in Stast i when t o, A B0odo constant c= 48000

Put c u,000 in we get, А е 0,05 t -0,065も A e ニー40,000 e -0.065も Diviele, uwhole equedtion by, e , we get, uno 月--yo ooo 48000 - .065も A = 니8000e Afłes Five yeaš ie t 5, (o.osS) x5 - 4O,00 O 66 433·4712-yo000 A 26 433 4712 Round ff: | A = 26433.47