Question

Avery invested $2,100 in an account paying an interest rate of 7 7/8% compounded continuously. Morgan invested $2,100 in an account paying an interest rate of 8 1/4 % compounded annually. After 12 years, how much more money would Morgan have in her account than Avery, to the nearest dollar?

Answer 1

`\$34`

Explanation:

step 1

Avery

we know that

The formula to calculate continuously compounded interest is equal to

`A=P(e)^(rt)`

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

e is the mathematical constant number

we have

`t=12\ years\\ P=\$2,100\\ r=7 7/8\%=7.875\%=0.07875`

substitute in the formula above

`A=\$2,100(e)^(0.07875*12)=\$5,402.91`

step 2

Morgan

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=12\ years\\ P=\$2,100\\ r=8 1/4\%=8.25\%=0.0825\\n=1`

substitute in the formula above

`A=\$2,100(1+(0.0825)/(1))^(1*12)=\$5,436.94`

step 3

Find the difference

`\$5,436.94-\$5,402.91=\$34.03`

To the nearest dollar

`\$34.03=\$34`