Sarah is going to invest in an account paying an interest rate of 5.3% compounded quarterly. How much would Sarah need to invest, to the nearest dollar, for the value of the account to reach 1,030 in 5 years?

Solution

S a r ah 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 5.3% 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 S a r ah 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 1, 030 in 5 ye a rs ?

Principal : 791.6

Solution steps

Translate the problem into an equation:

1030 = P (1 + \frac{0.053}{4})^{4 \cdot 5}

Solve for

P, 1030 = P (1 + \frac{0.053}{4})^{4 \cdot 5} : P = 791.6

Principal : 791.6