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

a.$7,096

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(((1.03) ^(12)-1 )/(0.03) )\\\\=500((1.42576-1)/(0.03) )\\\\=500((0.42576)/(0.03)) \\=$7,096`

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