Question

Ken planned to make monthly deposits in to a saving account at a nominal rate of 3% compounded monthly for 180 months. The amount of deposit is k at the end of the k th month, where k = 1, 2, ..., 180. However, he was unemployed for a short period of time, so he missed the 1st through 9th payments. He made the rest of the payments as planned. How much does Ken have in his saving account at the end of the 180th month after the last deposit?

(a) 18,941-18,950

(b) 18,951-18,960

(c) 18,961-18,970

(d) 18,971-18,980

(e) 18,931-18,940

Answer 1

Answer: (a) 18,941-18,950

Annual rate = 3%. So, monthly rate is 3/12 = 0.25%.

Ken's Saving at the end of 180th month = sum ( FV of Ken's 1st month saving at the 180th month +

FV of Ken's 2nd month saving at the 180th month +

FV of Ken's 3rd month's saving at the 180th month +

FV of Ken's 4th month's saving at the 180th month +

.... till

FV of Ken's 180th month saving at the 180th month)

Ken missed payments in the first 9-month. So, the value of saving is 0 for the first 9 months.

• FV of Ken's 10th Payment at the end of the 180th month.

FV = 10th payment + Interest accrued on 10th Payment.

10th payment = $10. While interest accrued on it is calculated by...

Interest = 10((1+R)N -1). Where R = Interest rate = 0.25% and N is difference between last period and invested period which is 170. [180th - 10th = 170].

Putting value in the equation we will get 10((1+0.0025)170 - 1) = $5.29.

So, FV of 10th deposit is $10 + $5.29 = $15.29.

Similarly, we can calculate the same for all other periods until the 180th month.

Which comes at $18,946.62.

Please find the attachment for detailed calculation and formula in the image below: