Question

Please answer the following time value of money questions below. Charting out each of the problem elements (ex. N = 10, PV = 500, etc.) will not only help you in answering the questions but will also assist me in following your calculations.

1. What is the present value of a 10-year annuity of $400 per year if the annual interest rate is 3.5%?

2. What will an investment of $2,500 today be worth in 15 years at an interest rate of 2.5% compounded semi-annually?

Answer 1

> What is the present value of a 10-year annuity of $400 per year if the annual interest rate is 3.5%?

PV = A * PVIFA,R,N

Where,

A = Annuity = $400

PVIFA,R,N = present value interest factor annuity, N,R

N = Number of periods = 10

R = Interest rate = 3.5%

PV = $400 * PVIFA,3.5%,10

PV = $400 * 8.3166 = 3326.64

Present value = $3326.64

> What will an investment of $2,500 today be worth in 15 years at an interest rate of 2.5% compounded semi-annually?

FV= PV * FVIF,R,N

FV = Future Value

PV = Present value = $2500

FVIF = Future Value interest factor

R = interest rate for semi annual period = 2.5% / 2 = 1.25%

N = number of period compounded = 15*2 =30

FVIF,1.25%,30 = (1+1.25%)^30= 1.4516

FV = 2500 * 1.4516 = $3629

Worth in 15 years = $3629