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# Calculating the amount of annual deposits

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P1
Deposits to accumulate future sums. For each of the cases shown in the following table, determine the amount of equal, annual, end of year deposits necessary to accumulate the given sum at the end of specified period, assuming stated annual interest rate.
Case Sum to be Accumulation
Accumulated period (years) Interest Rate
A \$5000 3 12%
B 100,000 20 7
C 30,000 8 10
D 15,000 12 8

P 2
Creating a retirement fund. To supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate \$220,000 by the end of 42 years from today. You plan to make equal, end-of-year deposits into an account paying 8% annual interest.
a. How large must the annual deposits be to create \$220,000 fund by the end of 42 years?
b. If you can afford to deposit \$600 per year into the account, how much will you have accumulated by the end of forty-second year?

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#### Solution Preview

Problem 1
Case A
Sum to be accumulated=S=\$5000
Number of periods=n=3
Interest rate=i=12%
Periodic payment=R=?

We know that sum of ordinary annuity is given by
S=R/i*((1+i)^n-1)
5000=R/12%*((1+12%)^3-1)
5000=R/12%*(0.404928)
5000=3.3744R
R=5000/3.3744=\$1481.75

Case B
Sum to be accumulated=S=\$100000
Number of periods=n=20
Interest rate=i=7%
Periodic payment=R=?

We know that ...

#### Solution Summary

There are two problems. Solutions to these problems depict the steps to calculate equal, annual, year end deposits sufficient enough to meet the given target.

\$2.19