An online bank is offering to pay 0.30% interest per month on deposits. Your local bank offers to pay 0.70% interest quarterly (every 3 months). Which is the higher interest rate?

The higher interest rate is 0.3% monthly rather than 0.7% quarterly

Explanation:

Equivalent Rates of Interest

Rates of interest are related to time. If we are given a specific monthly rate r, it can be found an equivalent rate in another time base. But it depends on the type of interest we're working with (simple or compound)

If we have a r=0.3% per month, we can find the equivalent quarterly rate by simply multiplying by 3, if the investment is made on the simple interest type. In this case r = 0.3%*3 = 0.9% quarterly.

If we are working with compound interest, the equivalent rate is more complicated to find

(1+r)=(1+0.003)^3=1.0009003

We find

In both cases, the higher interest rate is 0.3% monthly rather than 0.7% quarterly

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you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%