Sarah is going to invest in an account paying an interest rate of 6.8% compounded quarterly. How much would Sarah need to invest, to the nearest dollar, for the value of the account to reach 6,500 in 20 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 6.8% 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 6, 500 in 20 ye a rs ?

Principal : 1687.47

Solution steps

Translate the problem into an equation:

6500 = P (1 + \frac{0.068}{4})^{4 \cdot 20}

Solve for

P, 6500 = P (1 + \frac{0.068}{4})^{4 \cdot 20} : P = 1687.47

Principal : 1687.47