Josue is going to invest in an account paying an interest rate of 3.1% compounded quarterly. How much would Josue need to invest, to the nearest hundred dollars, for the value of the account to reach 1,170 in 13 years?

Solution

J os u e 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 3.1% co m p o u n d e d q u a r t er l y . Ho w m u c h w o u l d J os u e 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 1, 170 in 13 ye a rs ?

Principal : 783.14

Solution steps

Translate the problem into an equation:

1170 = P (1 + \frac{0.031}{4})^{4 \cdot 13}

Solve for

P, 1170 = P (1 + \frac{0.031}{4})^{4 \cdot 13} : P = 783.14

Principal : 783.14