Question

# 3 year(s) ago, Vivian invested 38,683 dollars. She has earned and will earn compound interest of...

3 year(s) ago, Vivian invested 38,683 dollars. She has earned and will earn compound interest of 11.87 percent per year. In 3 year(s) from today, Vince can make an investment and earn simple interest of 13.17 percent per year. If Vince wants to have as much in 7 years from today as Vivian will have in 7 years from today, then how much should Vince invest in 3 year(s) from today?

2 year(s) ago, Liam invested 64,777 dollars. He has earned and will earn 11.16 percent per year in compound interest. If Xiomara invests 107,904 dollars in 1 year(s) from today and earns simple interest, then how much simple interest per year must Xiomara earn to have the same amount of money in 6 years from today as Liam will have in 6 years from today? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

1. The final value of Vivian's amount will be = 38683 x (1.1187)^10 = 118756.265. Hence, Vince needs to make this amount in a total of 4 years. If the amount he invests is A, then

A x (1 + 7 x 0.1317) = 118756.265.

A = 61791.0739

2. In 8 years total, the amount invested by Liam will become = 64777 x (1+0.116)^8 = 155859.898. So, in order to have this amount in a total of 5 years with simple interest (assume the rate is r):

155859.898 = 107904 x (1 + r x 5)

Hence, r = 8.888%