Question

Recently, More Money 4U offered an annuity that pays 6.3 % compounded monthly. If $ 1,576 is deposited into this annuity every month, how much is in the account after 4 years? How much of this is interest?

1. Type the amount in the account:$

2.Type the amount of interest earned: $

Answer 1

Given Interest rate = 6.3% per month

Total Time period, n = 4 years = 48 months

-> Suppose the payment in annuity is done at start of each month.

So, Principal in annuity was 1576 intially, So, P = 1576(initially)

The table below shows the amount for each and every month:

start principal	start balance	interest	end balance	end principal
$1,576.00	$1,576.00	$8.27	$1,584.27	$1,576.00
$3,152.00	$3,160.27	$16.59	$3,176.87	$3,152.00
$4,728.00	$4,752.87	$24.95	$4,777.82	$4,728.00
$6,304.00	$6,353.82	$33.36	$6,387.18	$6,304.00
$7,880.00	$7,963.18	$41.81	$8,004.98	$7,880.00
$9,456.00	$9,580.98	$50.30	$9,631.28	$9,456.00
$11,032.00	$11,207.28	$58.84	$11,266.12	$11,032.00
$12,608.00	$12,842.12	$67.42	$12,909.54	$12,608.00
$14,184.00	$14,485.54	$76.05	$14,561.59	$14,184.00
$15,760.00	$16,137.59	$84.72	$16,222.31	$15,760.00
$17,336.00	$17,798.31	$93.44	$17,891.75	$17,336.00
$18,912.00	$19,467.75	$102.21	$19,569.96	$18,912.00
Year 1 End
$20,488.00	$21,145.96	$111.02	$21,256.98	$20,488.00
$22,064.00	$22,832.98	$119.87	$22,952.85	$22,064.00
$23,640.00	$24,528.85	$128.78	$24,657.63	$23,640.00
$25,216.00	$26,233.63	$137.73	$26,371.35	$25,216.00
$26,792.00	$27,947.35	$146.72	$28,094.08	$26,792.00
$28,368.00	$29,670.08	$155.77	$29,825.84	$28,368.00
$29,944.00	$31,401.84	$164.86	$31,566.70	$29,944.00
$31,520.00	$33,142.70	$174.00	$33,316.70	$31,520.00
$33,096.00	$34,892.70	$183.19	$35,075.89	$33,096.00
$34,672.00	$36,651.89	$192.42	$36,844.31	$34,672.00
$36,248.00	$38,420.31	$201.71	$38,622.02	$36,248.00
$37,824.00	$40,198.02	$211.04	$40,409.06	$37,824.00
Year 2 End
$39,400.00	$41,985.06	$220.42	$42,205.48	$39,400.00
$40,976.00	$43,781.48	$229.85	$44,011.33	$40,976.00
$42,552.00	$45,587.33	$239.33	$45,826.67	$42,552.00
$44,128.00	$47,402.67	$248.86	$47,651.53	$44,128.00
$45,704.00	$49,227.53	$258.44	$49,485.97	$45,704.00
$47,280.00	$51,061.97	$268.08	$51,330.05	$47,280.00
$48,856.00	$52,906.05	$277.76	$53,183.81	$48,856.00
$50,432.00	$54,759.81	$287.49	$55,047.30	$50,432.00
$52,008.00	$56,623.30	$297.27	$56,920.57	$52,008.00
$53,584.00	$58,496.57	$307.11	$58,803.67	$53,584.00
$55,160.00	$60,379.67	$316.99	$60,696.67	$55,160.00
$56,736.00	$62,272.67	$326.93	$62,599.60	$56,736.00
Year 3 End
$58,312.00	$64,175.60	$336.92	$64,512.52	$58,312.00
$59,888.00	$66,088.52	$346.96	$66,435.49	$59,888.00
$61,464.00	$68,011.49	$357.06	$68,368.55	$61,464.00
$63,040.00	$69,944.55	$367.21	$70,311.76	$63,040.00
$64,616.00	$71,887.76	$377.41	$72,265.17	$64,616.00
$66,192.00	$73,841.17	$387.67	$74,228.83	$66,192.00
$67,768.00	$75,804.83	$397.98	$76,202.81	$67,768.00
$69,344.00	$77,778.81	$408.34	$78,187.15	$69,344.00
$70,920.00	$79,763.15	$418.76	$80,181.90	$70,920.00
$72,496.00	$81,757.90	$429.23	$82,187.13	$72,496.00
$74,072.00	$83,763.13	$439.76	$84,202.89	$74,072.00
$75,648.00	$85,778.89	$450.34	$86,229.23	$75,648.00
Year 4 End

1.) So, Total Amount becomes = 86229.23

2.) So, Total Principal is = 75648 ( after 4 years)

Hence, Interest = 86229 - 75648 = 10581

-> Suppose payment in annuity is done at end of month. So, Initial Principal, P = 0

start principal	start balance	interest	end balance	end principal
$0.00	$0.00	$0.00	$1,576.00	$1,576.00
$1,576.00	$1,576.00	$8.27	$3,160.27	$3,152.00
$3,152.00	$3,160.27	$16.59	$4,752.87	$4,728.00
$4,728.00	$4,752.87	$24.95	$6,353.82	$6,304.00
$6,304.00	$6,353.82	$33.36	$7,963.18	$7,880.00
$7,880.00	$7,963.18	$41.81	$9,580.98	$9,456.00
$9,456.00	$9,580.98	$50.30	$11,207.28	$11,032.00
$11,032.00	$11,207.28	$58.84	$12,842.12	$12,608.00
$12,608.00	$12,842.12	$67.42	$14,485.54	$14,184.00
$14,184.00	$14,485.54	$76.05	$16,137.59	$15,760.00
$15,760.00	$16,137.59	$84.72	$17,798.31	$17,336.00
$17,336.00	$17,798.31	$93.44	$19,467.75	$18,912.00
Year 1 End
$18,912.00	$19,467.75	$102.21	$21,145.96	$20,488.00
$20,488.00	$21,145.96	$111.02	$22,832.98	$22,064.00
$22,064.00	$22,832.98	$119.87	$24,528.85	$23,640.00
$23,640.00	$24,528.85	$128.78	$26,233.63	$25,216.00
$25,216.00	$26,233.63	$137.73	$27,947.35	$26,792.00
$26,792.00	$27,947.35	$146.72	$29,670.08	$28,368.00
$28,368.00	$29,670.08	$155.77	$31,401.84	$29,944.00
$29,944.00	$31,401.84	$164.86	$33,142.70	$31,520.00
$31,520.00	$33,142.70	$174.00	$34,892.70	$33,096.00
$33,096.00	$34,892.70	$183.19	$36,651.89	$34,672.00
$34,672.00	$36,651.89	$192.42	$38,420.31	$36,248.00
$36,248.00	$38,420.31	$201.71	$40,198.02	$37,824.00
Year 2 End
$37,824.00	$40,198.02	$211.04	$41,985.06	$39,400.00
$39,400.00	$41,985.06	$220.42	$43,781.48	$40,976.00
$40,976.00	$43,781.48	$229.85	$45,587.33	$42,552.00
$42,552.00	$45,587.33	$239.33	$47,402.67	$44,128.00
$44,128.00	$47,402.67	$248.86	$49,227.53	$45,704.00
$45,704.00	$49,227.53	$258.44	$51,061.97	$47,280.00
$47,280.00	$51,061.97	$268.08	$52,906.05	$48,856.00
$48,856.00	$52,906.05	$277.76	$54,759.81	$50,432.00
$50,432.00	$54,759.81	$287.49	$56,623.30	$52,008.00
$52,008.00	$56,623.30	$297.27	$58,496.57	$53,584.00
$53,584.00	$58,496.57	$307.11	$60,379.67	$55,160.00
$55,160.00	$60,379.67	$316.99	$62,272.67	$56,736.00
Year 3 End
$56,736.00	$62,272.67	$326.93	$64,175.60	$58,312.00
$58,312.00	$64,175.60	$336.92	$66,088.52	$59,888.00
$59,888.00	$66,088.52	$346.96	$68,011.49	$61,464.00
$61,464.00	$68,011.49	$357.06	$69,944.55	$63,040.00
$63,040.00	$69,944.55	$367.21	$71,887.76	$64,616.00
$64,616.00	$71,887.76	$377.41	$73,841.17	$66,192.00
$66,192.00	$73,841.17	$387.67	$75,804.83	$67,768.00
$67,768.00	$75,804.83	$397.98	$77,778.81	$69,344.00
$69,344.00	$77,778.81	$408.34	$79,763.15	$70,920.00
$70,920.00	$79,763.15	$418.76	$81,757.90	$72,496.00
$72,496.00	$81,757.90	$429.23	$83,763.13	$74,072.00
$74,072.00	$83,763.13	$439.76	$85,778.89	$75,648.00
Year 4 End

1.) So, Total Amount becomes = 85778.89

2.) So, Total Principal is = 75648 ( after 4 years)

Hence, Interest = 85778.89 - 75648 = 10131