Question

2 year(s) ago, Goran invested 23,426 dollars. He has earned and will earn 4.64 percent per year in compound interest. If Grace invests 30,207 dollars in 3 year(s) from today and earns simple interest, then how much simple interest per year must Grace earn to have the same amount of money in 9 years from today as Goran will have in 9 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.

For each of the 4 investments described in the table, the investor would pay 4,300 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 TP > TL, 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 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
		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 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 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

Answer 1

1]

$23,426 was invested 2 years ago. This amount is compounded for 11 years (2 year till date, and a further 9 years from now. The future value of this amount, 9 years from today is calculated as :

future value = present value * (1 + interest rate)^{number of years}

future value = $23,426 * (1 + 4.64%)¹¹ = $38,580.97

If Grace invests $30,207 in 3 years from today, this amount earns simple interest for 6 years (9 years from now).

Ending amount 9 years from today = amount invested 3 years from today + (amount invested 3 years from today * simple interest rate * 6 years)

Ending amount 9 years from today = $30,207 + ( $30,207 * simple interest rate * 6)

This should equal $38,580.97, which is the amount that $23,426 invested 2 years ago will be worth 9 years from now.

Therefore :

$38,580.97 = $30,207 + ( $30,207 * simple interest rate * 6)

simple interest rate = ($38,580.97 - $30,207) / ($30,207 * 6)

simple interest rate = 0.0462