The compound interest formula is given by where is the accumulated amount, after an initial investment of dollars is invested for years, at annual interest rate , compounded times per year.Use the formula above to determine how long it will take an initial investment of 12,750 to grow to 36,975, if the account earns 11.5% interest per year, compounded quarterly. Round the solution to two decimal places.

Solution

T h e co m p o u n d in t eres t f or m u l a i s g i v e n b y w h ere i s t h e a cc u m u l a t e d am o u n t, a f t er an ini t ia l in v es t m e n t o f d o ll a rs i s in v es t e d f or ye a rs, a t ann u a l in t eres t r a t e, co m p o u n d e d t im es p er ye a r . U se t h e f or m u l a ab o v e t o d e t er min e h o w l o n g i t w i ll t ak e an ini t ia l in v es t m e n t o f 12, 750 t o g ro w t o 36, 975, i f t h e a cco u n t e a r n s 11.5% in t eres t p er ye a r, co m p o u n d e d q u a r t er l y . R o u n d t h e so l u t i o n t o tw o d ec ima l pl a ces .

Time : 9.39

Solution steps

Translate the problem into an equation:

36975 = 12750 (1 + \frac{0.115}{4})^{4 t}

Solve for

t, 36975 = 12750 (1 + \frac{0.115}{4})^{4 t} : t = 9.39081 \dots

Time : 9.39081 \dots

Round

9.39081 \dots

to the nearest 2 decimal places:

9.39

Time : 9.39