In order to be smart and calculative in personal finance matters, understanding the time value of money is an essential part of the learning process.

I will be posting a series of computation method related to time value of money on every Wednesday. Today, we
will learn to compute the value of a fixed sum of money invested regularly.

For instance, when you are setting aside a regular and fixed amount for saving, or unit trust dollar-cost-averaging strategy, there will be a constant sum of money invested at regular intervals. This series of cash flows is also known as an annuity.

## Common Problems

• You initiated a bank standing instruction to deduct RM200/month from your bank account for unit trust investment. The rate of return is about 15% p.a. How much is the total of your investment value after 5 years?
• You bought an endowment policy, paying total premium of RM988 per annum. Your agent told you that the insurance policy will mature in 25 years just on time for your retirement fund. The maturity benefit is projected at RM50,000?
• You apply a housing loan to fund the purchase of your first home. The house value is RM200,000. You paid RM20,000 down payment and finance the rest. Assuming the bank is offering you a flat loan rate of 5.8% p.a., how much is the monthly installments for loan tenure of 30 years?

Photo by wmjas

## Theory

This formula gives the Future Value of an annuity (assuming compound interest):

$FV_\mathrm{annuity} = {(1+r)^n-1 \over r} \cdot \mathrm{(payment\ amount)}$

where r = interest rate; n = number of periods.
Payment amount is normally indicated using “PMT”

For annuity calculations, we must first understand the timing of the payment.

Annuity due – An annuity with payments made at the beginning of each period. Also called advance payment annuity.

Examples:

• unit trust dollar-cost-averaging strategy
• paying tuition fees every month

Ordinary Annuity – A series of fixed payments made at the end of each period over a fixed amount of time.

Examples:

• housing loan installments
• car loan or hire purchase installments
• periodic interest on bonds where the coupon rates are fixed

## Solutions

Example 1:

You initiated a bank standing instruction to deduct RM200/month from your bank account for unit trust investment. The rate of return is about 15% p.a. How much is the total of your investment value after 5 years?

PV = 0
Beginning Mode
n = 5 x 12 = 60 months
i= 15% p.a./12 = 1.25% per month
PMT = RM200/month

Use this financial calculator:

FV = RM17,936.34

Example 2:

You bought an endowment policy, paying total premium of RM988 per annum. Your agent told you that the insurance policy will mature in 25 years just on time for your retirement fund. The maturity benefit is projected at RM50,000?

PV = 0
Beginning Mode
n = 25 years
PMT = RM988/month
FV = RM50,000
i = ?

i = 5.066% p.a.

Example 3:

You apply a housing loan to fund the purchase of your first home. The house value is RM200,000. You paid RM20,000 down payment and finance the rest. Assuming the bank is offering you a flat loan rate of 5.8% p.a., how much is the monthly installments for loan tenure of 30 years?

PV = RM180,000
End Mode
n = 30 years x 12 = 360 months
FV = 0
i = 5.8% p.a. = 0.48333% per month
PMT = ?

Monthly installment is RM1056.16.

## Exercise

You want to be a millionaire in 15 years time. Now, you already have a lump sum saving of RM50,000 in cash. After some deep consideration, you decided to invest the RM50,000 in a single-premium investment-linked insurance policy, which has a past history of giving 12% return per annum. Beside the insurance policy, you will also set aside RM1000 per month for unit trust investment using dollar-cost-averaging method. What is the minimum rate of return of the unit trust portfolio, so that you can achieve millionaire status in 15 years time?

Post your answer in the comment section. The first commenter who the right answers will get a special 3D birthday card sponsored by Pigeon Card.

## Previous Tutorial on Time Value of Money

KCLau

Personal finance author and trainer

### 4 replies to "Time Value of Money: Computing the Value of a Fixed Sum Invested Regularly"

• […] Computing the Value of a Fixed Sum Invested Regularly {Time Value of Money Tutorial} […]

• kelvin

KC, since you are an agent for Great Eastern, I have a question for you. Is good to invest money every month for the Great Eastern investment link fund, called GSR?

• KCLau

Hi Kevin,

I invest regularly in GSR. I like it more than unit trust.

• Garrett

Unit trust interest needed is 15.338% per annum

Solutions:
==================================
50,000 single lump insurance
PV = -50,000
Begining Mode
n = 15 years x 12 = 180 months
i = 12% p.a. = 1% per month
PMT = 0
FV = ?
= 299,790.10

1 Million = Unit Trust Investment FV + Insurance FV
Therefore, Unit Trust Investment FV
= 1 Million – Insurance FV
= 700,209.90

Unit Trust Investment
PV = 0
FV = 700,209.90
Beginning Mode
n = 15 years x 12 = 180 months
PMT = -1,000
i = ?
= 1.278185% per month
or 1.278185 x 12 = 15.33822% per annum