Question

1.3 year(s) ago, Vivian invested 67,464 dollars. She has earned and will earn compound interest of 11.18 percent per year. In 2 year(s) from today, Sang can make an investment and earn simple interest of 14.79 percent per year. If Sang wants to have as much in 6 years from today as Vivian will have in 6 years from today, then how much should Sang invest in 2 year(s) from today?

2.3 year(s) ago, Sang invested 69,076 dollars. He has earned and will earn 6.65 percent per year in compound interest. If Emily invests 81,254 dollars in 1 year(s) from today and earns simple interest, then how much simple interest per year must Emily earn to have the same amount of money in 6 years from today as Sang 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.

3.

For each of the 4 investments described in the table, the investor would pay 3,400 dollars today to purchase the investment. Each investment would have the annual return noted in the table and each investment would make a single, lump sum payment to the investor in the number of years from today noted in the table. If RD > RC and TL > TP, then which assertion is true? All annual returns and numbers of years from today when the single, lump sum payment will be made are greater than zero.

Investment	Annual return	Number of years from today when the single, lump sum payment will be made
C	RC	T
D	RD	T
L	R	TL
P	R	TP

		Investment D will make a larger single, lump sum payment in T years than investment C will make in T years, and investment L will make a larger single, lump sum payment in TL years than investment P will make in TP years
		Investment D will make a larger single, lump sum payment in T years than investment C will make in T years, and investment P will make a larger single, lump sum payment in TP years than investment L will make in TL years
		Investment C will make a larger single, lump sum payment in T years than investment D will make in T years, and investment L will make a larger single, lump sum payment in TL years than investment P will make in TP years
		Investment C will make a larger single, lump sum payment in T years than investment D will make in T years, and investment P will make a larger single, lump sum payment in TP years than investment L will make in TL years

Answer 1

Question 1:

(a) Total time period for Vivian = 1.3 + 6 = 7.3 years, r = 0.1118 and PV = 67,464

FV = PV*(1+r)^n = 67,464*(1+0.1118)^7.3 = 146,240.20

Now Sang will invest 2 years from now, so n = 7.3 -2 -1.3 = 4 years and r = 0.1479 Simple interest and FV = 146,240.20

For Simple Interest, FV = P*(1+nr)

146240.20 = P*(1+0.1479*4)

P = 91,882.51

Therefore Sang should invest $ 91,882.51 two years from today to have the same amount as Vivian

(b) Sang's Investment is 69,076 for 6+ 2.3 = 8.3 years at 6.65% compund interest

Its future value (FV) = PV*(1+r)^n = 69,076*(1+0.0665)^8.3 = 117,869.74

Emlie invests 81,254 whose FV should be  117,869.74 and n= 8.3-1-2.3 = 5 years

So, For simple interest, FV = P*(1+nr)

117869.74 = 81,254*(1+5r)

1.4506 = 1+5r

r = 0.09012 = 9.01%

Simple interest that Emily should earn = 9.01% = 0.0901

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