Question

: Payments of $ 670 are being made at the end of each month for 5 years at an interest of 8% compounded monthly. Calculate the Present Value.

Answer 1

Calculate the Present Value

We need to find the present value

Solution:

Given,

P = Principal value = $670

t = 5 years

r = 8% = 0.08

n = number of time interest compounded = 12

A = Amount

W e know the Formula for present value ,

Present Value of Annuity

$$= P \times [1 - ( 1 + \frac {r}{n}) ^ {- t \times n }] \times [ \frac {1 + \frac {r}{n}} {(\frac {r} {n})}]$$

$$= 670 \times [1 - ( 1 + \frac {0.08}{12}) ^ {- 5 \times 12 }] \times [ \frac {1 + \frac {0.08}{12}} {(\frac {0.08} {12})}]$$

$$= 670 \times [1 - ( 1 + {0.0066}) ^ {- 60}] \times [ \frac {1 +0.0066} {0.0066}]$$

$$= 670 \times 0.326 \times 152.51 = \$ 33,311.23$$

Answer : Present value = $33,311.23