Amira is going to invest in an account paying an interest rate of 2.4% compounded continuously. How much would Amira need to invest, to the nearest dollar, for the value of the account to reach 320 in 17 years?

Solution

A mi r a 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 2.4% 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 A mi r a 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 320 in 17 ye a rs ?

Principal : 212.79

Solution steps

Translate the problem into an equation:

320 = P e^{0.024 \cdot 17}

Solve for

P, 320 = P e^{0.024 \cdot 17} : P = 212.79

Principal : 212.79