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On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested $2,000 at 5 percent annual interest, compounded annually. The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?

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Answer:

$5

Explanation:

The value of investment after two years of investment by Tim  can be calculate using the following formula:

Value of investment= P(1+i)^n

n=number of years=2

i=annual interest=10%

P= amount invested by Tim initially=$1,000

value of investment=1,000(1+10%)^2

                                =1,000(1.21)

                                =1,210

Interest earned by tim over the two years=1,210-1,000=210

The value of investment after two years of investment by Lana can be calculate using the following formula:

Value of investment= P(1+i)^n

n=number of years=2

i=annual interest=5%

P= amount invested by Lana initially=$2,000

value of investment=2,000(1+5%)^2

                                =1,000(1.1025)

                                =2,205

Interest earned by Lana over the two years=2,205-2,000=205

Excess interest earned by Tim over Lana=210-205=$5

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