Bella invested 8,400 in an account paying an interest rate of 1.9% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach 9,890?

الحلّ

B e ll a in v es t e d 8, 400 in an a cco u n t p a y in g an in t eres t r a t e o f 1.9% co m p o u n d e d co n t in u o u s l y . A ss u min g n o d e p os i t s or w i t h d r a w a l s a re ma d e, h o w l o n g w o u l d i t t ak e, t o t h e n e a res t t e n t h o f a ye a r, f or t h e v a l u e o f t h e a cco u n t t o re a c h 9, 890 ?

Time : 8.59

خطوات الحلّ

Translate the problem into an equation:

9890 = 8400 e^{0.019 t}

9890 = 8400 e^{0.019 t}, t

حلّ لـ:

t = 8.59

Time : 8.59