Question

How would a decrease in the interest rate effect the present value of a lump sum, single amount problem (all other variables remain the same)?

Answer 1

A decrease in the interest rate would increase the present value of a lump sum.

Step-by-step explanation:

Higher interest rate represents higher expected rate of return. Higher interest rate would lead to a greater future value if a sum of money is invested. Conversely the present value will be lower at high interest rate since the discounting rate would be higher.

Similarly, if the interest rates fall, the future value of an invested amount will fall. But present value of a lump sum would rise with fall in the interest rates since the discounting rate would be less.

Future Value =
`A(1\ +\ r)^(n)`

Present Value =
`(Future\ amount)/((1\ +\ r)^(n) )`

Hence, a decrease in the interest rate would increase the present value of a lump sum with others variables remaining the same.