Owen is going to invest in an account paying an interest rate of 5.7% compounded continuously. How much would Owen need to invest, to the nearest hundred dollars, for the value of the account to reach 122,000 in 14 years?

Solution

Ow e n 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 5.7% 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 Ow e n 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 122, 000 in 14 ye a rs ?

Principal : 54927.88

Solution steps

Translate the problem into an equation:

122000 = P e^{0.057 \cdot 14}

Solve for

P, 122000 = P e^{0.057 \cdot 14} : P = 54927.88

Principal : 54927.88