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Monthly deposits with quarterly compounding, future amount

Short answer

Effective monthly rate = (1.025)^(1/3) - 1 = 0.8265%. First find FV after 5 years of monthly Rs 5,000: Rs 3,86,345. Then compound that amount 5 more years at 2.5% quarterly: F10 = 3,86,345 × (1.025)^20 = Rs 6,33,072.

What will be the amount at the end of 10 years if you deposit Rs 5000 per month for five years continuously if nominal interest rate is 10% compounded quarterly?

Approach

Deposits are monthly but interest is compounded quarterly, so find the equivalent interest rate per month, then compound the five-year amount for the next five years.

Nominal rate 10% compounded quarterly: i per quarter = 10%/4 = 2.5% Effective monthly rate: i_m = (1.025)^(1/3) − 1 = 0.8265% per month

 Deposits 5000 each month, months 1..60 (5 years)
 |-----------------------|-----------------------|
 0                       60                      120 months
 deposits ->             F5 = ?                  F10 = ?

Step 1: Amount at end of year 5

F5 = 5,000 (F/A, 0.8265%, 60) (1.008265)^60 = (1.025)^20 = 1.63862 (F/A, 0.8265%, 60) = (1.63862 − 1) / 0.008265 = 77.269 F5 = 5,000 × 77.269 = Rs 386,345

Step 2: Grow for the next 5 years (no deposits)

F10 = F5 (F/P, 2.5%, 20) = 386,345 × 1.63862 = Rs 633,072

Answer: Amount at the end of 10 years = about Rs 6.33 lakh (Rs 633,000).

✓ Answer checked by Claude Opus 5.5 (high effort)

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