Noah is going to invest in an account paying an interest rate of 7% compounded continuously. How much would Noah need to invest, to the nearest hundred dollars, for the value of the account to reach 12,900 in 10 years?

Solution

N o ah i s g o in g t o in v es t in an a cco u n t p a y in g an in t eres t r a t e o f 7% co m p o u n d e d co n t in u o u s l y . Ho w m u c h w o u l d N o ah n ee d t o in v es t, t o t h e n e a res t h u n d re d d o ll a rs, 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 12, 900 in 10 ye a rs ?

Principal : 6405.95

Solution steps

Translate the problem into an equation:

12900 = P e^{0.07 \cdot 10}

Solve for

P, 12900 = P e^{0.07 \cdot 10} : P = 6405.95

Principal : 6405.95