Question

2(30 points) You invest $x today at 8% APR compounded annually for 5 years (you invest only once). Your friend also invests some amount at the same time at 8% APR compounded annually for 5 years. However, she invests an additional amount equal to the accumulated interest at the end of each year. You both end up having the same amount at the end of 5 years. In order to achieve this, your initial investment must have been t times as much as your friends. What is t?

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Answer #1

Basically the firend is earning 4% APR

Hence, we can say that

x*(1+8%)^5=tx*(1+4%)^5

=>t=(1.08/1.04)^5

=>t=1.207680575

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