Question

Karina has two investment options for 40,000 she is saving for her future. One account pay 3.5% interest compound weekly and 3.2% compound daily. Which account will have the larger balance after 6 years?

Answer 1

Remember 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 the Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

Part 1

P=$40,000

r=3.5%=3.5/100=0.035

n=52 (in one year there are 52 weeks)

t=6 years

substitute

`\begin{gathered} A=40,000(1+(0.035)/(52))^(52*6) \\ \\ A=40,000((52.035)/(52))^(312) \\ \\ A=\$49,343.64 \end{gathered}`

Part 2

we have

P=$40,000

r=3.2%=3.2/100=0.032

n=365 (in one year there are 365 days)

t= 6 years

substitute

`\begin{gathered} A=40,000(1+(0.032)/(365))^(365*6) \\ \\ A=40,000((365.032)/(365))^(2190) \\ \\ A=\$48,466.41 \end{gathered}`

therefore

The answer is

The account that pays 3.5% compounded weekly