13-Solved problems: Deposit value for uniform series.

Last Updated on September 7, 2026 by Maged kamel

Deposit value for uniform series, A.

The first solved problem is to find the deposit value A for a uniform series in terms of n, I, and F.

The title is College Savings Plan: Find A, given F, N, and I. F is the future value, N is the number of years, deposits, and Time periods, and I is the interest.

You want to set up a college savings plan for your daughter, who is currently 10 and will attend college at age 18.

She needs at least $100,000 in the bank, which she must deposit.

The bank offers an interest rate of 7%. Deposits are made in equal amounts at the end of each year. This is the case for the uniform series, A. The factor used (A/F) is called the sinking fund factor.

You need $100,000. This sum is the future value; A is unknown, given n and interest rate i%. The N value is 8 deposits over 8 years, and i = 7%.

The first solved problem: find the deposit value for a uniform series -using the Cash flow method.

Suppose we use the Cash flow Moment method at a pivot point, t = 0. The Moment caused by the future value F will be Equivalent to that caused by the uniform series of deposits at the same point.

To get the Moment due to the future value, it equals F as a positive number, and the point is on the left side of F; the Moment arm to the pivot point at t=0 will be (1+i)^-8. The Moment value is $100,000 × (1.07)^-88}$

For the Moment, this is caused by the uniform series of deposits. It will be -A*(1+i)-8 + (-A)*(1+i)^7, and so on until we complete the deposit Expression. The sum of moments is zero. After adjustments, the result is A multiplied by 5.97129.

The product of A*5.97129 will equal $100,000/(1.07) 8=$100,000/1.7181. We simplify the result to 100,000/10.2598 = $974.78. The final value of A is $974.78, payable at the end of each year for 8 years to achieve a future value of $100,000.

Use the Cash Flow Moment at the pivot point t=0.

The first problem solved is finding the deposit value for a uniform series using the A/F method.

The second method uses the equation, A =$100,000*(A/F,7%,8)=$9746.71. The value is the same as estimated by the Cash Flow Moment method.

A/F can be estimated by using the formula, A/F=(i)/((1+i)^n-1), i=7%,n=8. We substitute to get A/F as (0.07)/((1.07)^8-1))=0.09746. The value will be multiplied by $100,000 to get the A value. A value will be $100,000*0.09746=$9746.78.

A table was used to determine the deposit value for the uniform series with i = 7%.

The next method uses the interest rate table. We use the 7% interest rate table; our n value is 8. We need to find the A/F value. Check the sinking fund factor A/F to find A in terms of F. We go vertically and find the intersection with n=8; we get 0.0975.

This number matches the previous calculations.

Use the Excel PMT function to find the deposit amount for the uniform series.

Another way to get the value of A/F is by using the Excel function PMT. The inputs are 0.07, Nper is 8 deposits, PV stands for present value, 0, FV stands for the future value, which is $100,000, and type is 0. The A value is negative because the uniform series is an outflow.

If we use an Excel sheet, use cells. Cell C19 has an interest rate of 7%. The N periods are 8. Cell C21 is for a

Future value F is equal to 100,000. In the last cell, C23, we can get the A value as a negative number. I have taken a screenshot of the cell.

PMT(C19,C20,0,+C21). The A value can be obtained using the Excel sheet.

A second solved problem is finding A for a uniform series: use the Cash flow Moment.

Check another problem: 2.12, paying off an education loan. Find A, Given P, I, and N. This is another way to get A, but this Time in terms of P,  where P is the present value. You borrow from the bank to finance your educational expenses. The loan should be returned to the bank within the next five years.

The interest rate is 6% per year. The payment should be in equal annual installments. The loan will be paid off over five years. As we know, for a uniform series, payments begin one year after the loan is taken out.

The first installment is due a year later. Estimating the amount of the annual installment A is required. Refer to Figure 2.20. This solved problem requires estimating A in terms of P, while the previously solved problem requires estimating A in terms of F.

In this solved problem, I and n are given. First, we will use the moment-of-cash-flow method to estimate the Moment of Cash flow about the pivot point. Take the pivot point at Time t=0. If P is pointing upwards, then it is +P.

The Moment arm for P is (1+i)^0; whether from the right or the left, P coincides with the point, and the arm length is equal to 1.

. The sum of moments is equal to zero. P will be on the L.H.S., and the product of A by the arm will be set as the R.H.S., with a changing sign.
The negative exponents are considered fractions.

The equation is modified as we can see , P=A*(1/(1.06)+1/1.06^2)+1/(1.06)^3++1/(1.06)^4+1/(1.06)^5)). The P-value is $21061.82. We equate it to the correct value (4.2123)*A. Finally, the A value is $5000.

This is another example that uses a pivot at t = 1; the sum of moments is shown based on the selected pivot point. Please refer to the right side of the slide picture for a comparison between Cash flow moments based on a pivot point at t=0 and at a pivot point at t=1. Finally, the A value is $5000.

Use the Expression of A/P to find the deposit value A for a uniform series.

We use an equation in which A = P(A/P, i, n), with P given and A unknown. P=$21061.82. A/P value can be obtained from the known equation as equal to (i*(1+i)^n/(1+i)^n-1)). The A/P value is equal to 0.2374. A/P will be multiplied by P. The deposit value A =21061*0.2374=$5000. The same value for A matches the previous calculation at the Moment of Cash flows.

The PDF file used for the post can be viewed or downloaded from the following document.

This relates to the previously solved problem value for uniform series deposits.

This is a good link -Engineering Economy. A good reference