Question

Q1. If money can be invested at 0.6% per month, which has the greater economic value: $5230 on a specific date or $5500 exactly five months later? At what rate (per month) would the two amounts be economically equivalent?

Answer 1

Answer:

question asked whether to take $ 5230 on a specific date or to take $ 5500 after 5 months:

To answer this we have to calculated the present value of $ 5500 which is to be received after 5 months:

here we have future value $ 5500 so precisely we have to calculate present value. Let's assume X is the present value.

formula to calculate PV = FV / (1 + r )^t

FV = the future value of money
PV = the present value
r = the interest rate
t = the number of months to take into consideration

PV = 5500 / (1+0.6%)⁵

We will get figure of $ 5337. 93.

hence the present value of $ 5500 is greater than $ 5230 so we should $ 5500 after 5 months.

Calculation of rate at which $ 5500 will become equivalent to $ 5230

Using above formula:

PV = FV / (1 + r )^t

5230 = 5500 / (1 + r)⁵

(1+r)5 = 5500/5230

(1+r)⁵ = 1.05

(1+r) = (1.05)^1/5

(1+r) = 1.0098

r = 1.0098- 1

r = 0.0098 or 0.98% approx.

Hence at 0.98 % rate $ 5500 will become equivalent to $ 5230