Jacob is going to invest in an account paying an interest rate of 2.6% compounded continuously. How much would Jacob need to invest, to the nearest dollar, for the value of the account to reach 10,500 in 18 years?

Solution

J a co b 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 2.6% 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 J a co b 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 10, 500 in 18 ye a rs ?

Principal : 6575.66

Solution steps

Translate the problem into an equation:

10500 = P e^{0.026 \cdot 18}

Solve for

P, 10500 = P e^{0.026 \cdot 18} : P = 6575.66

Principal : 6575.66