Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra 28,000 over the next 3 years. What amount must be deposited quarterly into an account that earns 5.1% interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.

Solution

S u pp ose yo u^{'} d l ik e t o s a v e e n o ug h m o n ey t o p a y c a s h f or yo u r n e x t c a r . T h e g o a l i s t o s a v e an e x t r a 28, 000 o v er t h e n e x t 3 ye a rs . Wha t am o u n t m u s t b e d e p os i t e d q u a r t er l y in t o an a cco u n t t ha t e a r n s 5.1% in t eres t, co m p o u n d e d q u a r t er l y, in or d er t o re a c h yo u r g o a l ? R o u n d yo u r an s w er t o t h e n e a res t ce n t, i f n ecess a ry .

Amount : 32597.56

Solution steps

Translate the problem into an equation:

A = 28000 (1 + \frac{0.051}{4})^{4 \cdot 3}

28000 (1 + \frac{0.051}{4})^{4 \cdot 3} = 32597.55701 \dots

Round to the nearest hundredth:

32597.56

Amount : 32597.56