Aaliyah is going to invest in an account paying an interest rate of 5% compounded continuously. How much would Aaliyah need to invest, to the nearest hundred dollars, for the value of the account to reach 181,000 in 19 years?

Solution

A a l i y 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 5% 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 A a l i y 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 181, 000 in 19 ye a rs ?

Principal : 70000.13

Solution steps

Translate the problem into an equation:

181000 = P e^{0.05 \cdot 19}

Solve for

P, 181000 = P e^{0.05 \cdot 19} : P = 70000.13

Principal : 70000.13