Keilantra is saving money and plans on making quarterly contributions into an account earning an annual interest rate of 3.2% compounded quarterly. If Keilantra would like to end up with dollar sign, 61, comma, 00061, 000 after 6 years, how much does she need to contribute to the account every quarter, to the nearest dollar? Use the following formula to determine your answer.

Solution

Ke i l an t r a i s s a v in g m o n ey an d pl an s o n makin g q u a r t er l y co n t r ib u t i o n s in t o an a cco u n t e a r nin g an ann u a l in t eres t r a t e o f 3.2% co m p o u n d e d q u a r t er l y . I f Ke i l an t r a w o u l d l ik e t o e n d u p w i t h d o ll a r s i g n, 61, co mma, 00061, 000 a f t er 6 ye a rs, h o w m u c h d oes s h e n ee d t o co n t r ib u t e t o t h e a cco u n t e v ery q u a r t er, t o t h e n e a res t d o ll a r ? U se t h e f o ll o w in g f or m u l a t o d e t er min e yo u r an s w er .

Principal : 0.21

Solution steps

Translate the problem into an equation:

\frac{1}{4} = P (1 + \frac{0.032}{4})^{4 \cdot 6}

Solve for

P, \frac{1}{4} = P (1 + \frac{0.032}{4})^{4 \cdot 6} : P = 0.21

Principal : 0.21