Question

At the end of each quarter, Patti deposits $500 into an account that pays 12% interest compounded quarterly. How much will Patti have in the account in three years?a.$7,096.b.$7,129.c.$7,213.d.$8,880.

Answer 1

Answer:

a.$7,096

Step-by-step explanation:

• total amount A =  s(\frac{(1+\frac{r}{n}) ^{n*t}-1 }{\frac{r}{n} } )[/tex]

[this is the formula used when certain amount is added at regular intervals and if the interest is COMPOUNDED]

(here,

s=deposit added at the end of each quarter=  $500

n= number of times interest is compounded per unit 't'=4

t=total time = 3 years

r=interest rate ( expressed in decimal or fraction not in %) = 12/100 = 0.12 )

• A= 500(\frac{(1+\frac{0.12}{4}) ^{4*3}-1 }{\frac{0.12}{4} } )[/tex]

• by solving further,

A  $=500(\frac{(1.03) ^{12}-1 }{0.03} )\\\\=500(\frac{1.42576-1}{0.03} )\\\\=500(\frac{0.42576}{0.03}) \\= 7,096$

( [1.03]^12= 1.42576 ( approximately) { use calculator for exact values})