Question

After 6 years, what is the total amount of a compound interest investment of $35,000 at 4% interest, compounded quarterly? $37,153.21 $39,438.88 $44,440.71 $56,295.30

Answer 1

we know that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

`t=6\ years\\ P=\$35,000\\ r=0.04\\n=4`

substitute in the formula above

`A=35,000(1+(0.04)/(4))^(4*6)`

`A=35,000(1.01)^(24)`

`A=\$44,440.71`

therefore

the answer is the option

`\$44,440.71`

Answer 2

The given rate of interest is 4% compounded quarterly. This is a nominal rate of interest. To make it an effective rate of interest,

`i_(eff)` =
`(1 + (i)/(m) )^(m) -1`, where m is the number of periods in a year. There are 4 quarters in a year, so m =4. So,

`i_(eff)` =
`(1 + (0.04)/(4) )^(4) -1`= 0.0406

The working equation is

`F = P (1 + i_(eff))^(n)`, where n=6, P = $35000,

`F = $35000 (1 + 0.0406))^(6)`

F = $44,440.71