Ian is going to invest in an account paying an interest rate of 5% compounded continuously. How much would Ian need to invest, to the nearest hundred dollars, for the value of the account to reach 108,000 in 6 years?

Solution

I an 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 I an 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 108, 000 in 6 ye a rs ?

Principal : 80008.37

Solution steps

Translate the problem into an equation:

108000 = P e^{0.05 \cdot 6}

Solve for

P, 108000 = P e^{0.05 \cdot 6} : P = 80008.37

Principal : 80008.37