Lamonte is going to invest in an account paying an interest rate of 4% compounded continuously. How much would Lamonte need to invest, to the nearest cent, for the value of the account to reach 12,300 in 8 years?

Solution

L am o n t e 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 4% 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 L am o n t e n ee d t o in v es t, t o t h e n e a res t ce n t, 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, 300 in 8 ye a rs ?

Principal : 8931.63

Solution steps

Translate the problem into an equation:

12300 = P e^{0.04 \cdot 8}

Solve for

P, 12300 = P e^{0.04 \cdot 8} : P = 8931.63

Principal : 8931.63