William is going to invest in an account paying an interest rate of 2.5% compounded continuously. How much would William need to invest, to the nearest cent, for the value of the account to reach 4,700 in 14 years?

Solution

Wi ll iam 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 2.5% 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 Wi ll iam 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 4, 700 in 14 ye a rs ?

Principal : 3312.03

Solution steps

Translate the problem into an equation:

4700 = P e^{0.025 \cdot 14}

Solve for

P, 4700 = P e^{0.025 \cdot 14} : P = 3312.03

Principal : 3312.03