Grayson is going to invest in an account paying an interest rate of 4% compounded continuously. How much would Grayson need to invest, to the nearest dollar, for the value of the account to reach 15,000 in 5 years?

Solution

G r a yso 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 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 G r a yso n n ee d t o in v es t, t o t h e n e a res t d o ll a r, 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 15, 000 in 5 ye a rs ?

Principal : 12280.96

Solution steps

Translate the problem into an equation:

15000 = P e^{0.04 \cdot 5}

Solve for

P, 15000 = P e^{0.04 \cdot 5} : P = 12280.96

Principal : 12280.96