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Monthly deposits, quarterly compounding, balance at year 8

Short answer

Monthly rate from 12% compounded quarterly: (1.03)^(1/3)-1 = 0.99016%. FV after 5 years of Rs 2,000/month: Rs 1,62,824. Compound this for 3 years at 3% quarterly: F8 = 1,62,824 × (1.03)^12 = Rs 2,32,148.

If you make equal monthly deposits of Rs 2000 into the bank for five years, saving accounts that pays interest rate of 12% compounded quarterly. Find the balance at the end of 8 year?

Approach

Deposits are monthly but interest is compounded quarterly (12% nominal). Convert to an equivalent monthly rate, find the amount after 5 years, then compound it for 3 more years.

  • Quarterly rate = 12%/4 = 3%
  • Monthly rate: i_m = (1.03)^(1/3) − 1 = 0.99016% per month
 2000 each month (60 deposits)
 |------------------|---------------|
 0                  5 yr            8 yr
                    F5 = ?          F8 = ?

Step 1: Amount at end of year 5

(F/A, 0.99016%, 60) = [(1.03)²⁰ − 1] / 0.0099016 = (1.80611 − 1)/0.0099016 = 81.41 F5 = 2,000 × 81.41 = Rs 162,824

Step 2: Compound for 3 years (12 quarters)

F8 = F5 (F/P, 3%, 12) = 162,824 × 1.42576 = Rs 232,148

Answer: Balance at the end of year 8 = about Rs 232,150.

✓ Answer checked by Claude Opus 5.5 (high effort)

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