Question

If I make a deposit today that will increase in value to $100 at the end of the year, what interest rate will allow me to deposit the least amount to reach my goal? 3.8%, 2.6%, 2.9%, 3.6% and 3.4% ?

Answer 1

Ans:

Let x be the amount to be deposited today.

Present Value Future value / ( 1+r)ⁿ  

If n = number of years = 1

if interest rate = 3.8%

Present Value = 100 / (1+ 3.8/100)¹

= 100 / (1.038)

= 100 * 0.9634

= $ 96.34

if interest rate = 2.6%

Present Value = 100 / (1+ 2.6/100)¹

= 100 / (1.026)

= 100 * 0.9746

= $ 97.46

if interest rate = 2.9%

Present Value = 100 / (1+ 2.9/100)¹

= 100 / (1.029)

= 100 * 0.9718

= $ 97.18

if interest rate = 3.6%

Present Value = 100 / (1+ 3.6/100)¹

= 100 / (1.036)

= 100 * 0.9652

= $ 96.52

if interest rate = 3.4%

Present Value = 100 / (1+ 3.4/100)¹

= 100 / (1.034)

= 100 * 0.9671

= $ 96.71

Among all the values , the least amount that is invested to make 100 is $ 96.33 for interest rate of 3.8%